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3.3: The Derivative as a Function
https://math.libretexts.org/Courses/Coastline_College/Math_C180%3A_Calculus_I_(Tran)/03%3A_Derivatives/3.03%3A_The_Derivative_as_a_Function
The derivative of a function $f(x)$ is the function whose value at $x$ is $f′(x)$ . The graph of a derivative of a function f(x) is related to the graph of f(x). Where (f(x) has a tangent line wi...The derivative of a function $f(x)$ is the function whose value at $x$ is $f′(x)$ . The graph of a derivative of a function f(x) is related to the graph of f(x). Where (f(x) has a tangent line with positive slope, f′(x)>0. Where (x) has a tangent line with negative slope, f′(x)<0. Where f(x) has a horizontal tangent line, f′(x)=0. If a function is differentiable at a point, then it is continuous at that point.
3.3: The Derivative as a Function
https://math.libretexts.org/Courses/SUNY_Geneseo/Math_221_Calculus_1/03%3A_Derivatives/3.03%3A_The_Derivative_as_a_Function
The derivative of a function f(x) is the function whose value at x is f′(x). The graph of a derivative of a function f(x) is related to the graph of f(x). Where (f(x) has a tangent line with positive ...The derivative of a function f(x) is the function whose value at x is f′(x). The graph of a derivative of a function f(x) is related to the graph of f(x). Where (f(x) has a tangent line with positive slope, f′(x)>0. Where (x) has a tangent line with negative slope, f′(x)<0. Where f(x) has a horizontal tangent line, f′(x)=0. If a function is differentiable at a point, then it is continuous at that point.
3.2: The Derivative as a Function
https://math.libretexts.org/Courses/Mission_College/Math_3A%3A_Calculus_I_(Kravets)/03%3A_Derivatives/3.02%3A_The_Derivative_as_a_Function
The derivative of a function f(x) is the function whose value at x is f′(x). The graph of a derivative of a function f(x) is related to the graph of f(x). Where (f(x) has a tangent line with positive ...The derivative of a function f(x) is the function whose value at x is f′(x). The graph of a derivative of a function f(x) is related to the graph of f(x). Where (f(x) has a tangent line with positive slope, f′(x)>0. Where (x) has a tangent line with negative slope, f′(x)<0. Where f(x) has a horizontal tangent line, f′(x)=0. If a function is differentiable at a point, then it is continuous at that point.
2.8: The Derivative as a Function
https://math.libretexts.org/Courses/Southwestern_College/Business_Calculus/02%3A_Unit_2-_Pre-Calculus_and_Limits/2.08%3A_The_Derivative_as_a_Function
The derivative of a function f(x) is the function whose value at x is f′(x). The graph of a derivative of a function f(x) is related to the graph of f(x). Where (f(x) has a tangent line with positive ...The derivative of a function f(x) is the function whose value at x is f′(x). The graph of a derivative of a function f(x) is related to the graph of f(x). Where (f(x) has a tangent line with positive slope, f′(x)>0. Where (x) has a tangent line with negative slope, f′(x)<0. Where f(x) has a horizontal tangent line, f′(x)=0. If a function is differentiable at a point, then it is continuous at that point.
3.2: The Derivative as a Function
https://math.libretexts.org/Courses/Monroe_Community_College/MTH_210_Calculus_I_(Professor_Dean)/professor_playground/3.2%3A_The_Derivative_as_a_Function
As we have seen, the derivative of a function at a given point gives us the rate of change or slope of the tangent line to the function at that point. The derivative function gives the derivative of a...As we have seen, the derivative of a function at a given point gives us the rate of change or slope of the tangent line to the function at that point. The derivative function gives the derivative of a function at each point in the domain of the original function for which the derivative is defined. To understand this notation better, recall that the derivative of a function at a point is the limit of the slopes of secant lines as the secant lines approach the tangent line.
3.2: The Derivative as a Function
https://math.libretexts.org/Courses/Mission_College/Math_3A%3A_Calculus_1_(Sklar)/03%3A_Derivatives/3.02%3A_The_Derivative_as_a_Function
The derivative of a function f(x) is the function whose value at x is f′(x). The graph of a derivative of a function f(x) is related to the graph of f(x). Where (f(x) has a tangent line with positive ...The derivative of a function f(x) is the function whose value at x is f′(x). The graph of a derivative of a function f(x) is related to the graph of f(x). Where (f(x) has a tangent line with positive slope, f′(x)>0. Where (x) has a tangent line with negative slope, f′(x)<0. Where f(x) has a horizontal tangent line, f′(x)=0. If a function is differentiable at a point, then it is continuous at that point.
3.2: The Derivative as a Function
https://math.libretexts.org/Courses/College_of_Southern_Nevada/Calculus_(Hutchinson)/03%3A_Differentiation/3.02%3A_The_Derivative_as_a_Function
As we have seen, the derivative of a function at a given point gives us the rate of change or slope of the tangent line to the function at that point. The derivative function gives the derivative of a...As we have seen, the derivative of a function at a given point gives us the rate of change or slope of the tangent line to the function at that point. The derivative function gives the derivative of a function at each point in the domain of the original function for which the derivative is defined. To understand this notation better, recall that the derivative of a function at a point is the limit of the slopes of secant lines as the secant lines approach the tangent line.
2.9: The Derivative as a Function
https://math.libretexts.org/Courses/City_College_of_San_Francisco/CCSF_Calculus/02%3A_Learning_Limits/2.09%3A_The_Derivative_as_a_Function
This section explains the derivative as a function, focusing on how the derivative varies across the domain of a function. It describes how the derivative itself can be viewed as a new function that g...This section explains the derivative as a function, focusing on how the derivative varies across the domain of a function. It describes how the derivative itself can be viewed as a new function that gives the slope of the original function at any point. The section also covers the graphical interpretation, showing how the behavior of the derivative reflects changes in the original function's slope, such as increasing or decreasing trends.
3.2: The Derivative as a Function
https://math.libretexts.org/Courses/Monroe_Community_College/MTH_210_Calculus_I_(Professor_Dean)/Chapter_3%3A_Derivatives/3.2%3A_The_Derivative_as_a_Function
As we have seen, the derivative of a function at a given point gives us the rate of change or slope of the tangent line to the function at that point. The derivative function gives the derivative of a...As we have seen, the derivative of a function at a given point gives us the rate of change or slope of the tangent line to the function at that point. The derivative function gives the derivative of a function at each point in the domain of the original function for which the derivative is defined. To understand this notation better, recall that the derivative of a function at a point is the limit of the slopes of secant lines as the secant lines approach the tangent line.
3.2: The Derivative as a Function
https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/03%3A_Derivatives/3.02%3A_The_Derivative_as_a_Function
The derivative of a function f(x) is the function whose value at x is f′(x). The graph of a derivative of a function f(x) is related to the graph of f(x). Where (f(x) has a tangent line with positive ...The derivative of a function f(x) is the function whose value at x is f′(x). The graph of a derivative of a function f(x) is related to the graph of f(x). Where (f(x) has a tangent line with positive slope, f′(x)>0. Where (x) has a tangent line with negative slope, f′(x)<0. Where f(x) has a horizontal tangent line, f′(x)=0. If a function is differentiable at a point, then it is continuous at that point.
3.3: The Derivative as a Function
https://math.libretexts.org/Courses/Coastline_College/Math_C180%3A_Calculus_I_(Nguyen)/03%3A_Derivatives/3.03%3A_The_Derivative_as_a_Function
The derivative of a function $f(x)$ is the function whose value at $x$ is $f′(x)$ . The graph of a derivative of a function f(x) is related to the graph of f(x). Where (f(x) has a tangent line wi...The derivative of a function $f(x)$ is the function whose value at $x$ is $f′(x)$ . The graph of a derivative of a function f(x) is related to the graph of f(x). Where (f(x) has a tangent line with positive slope, f′(x)>0. Where (x) has a tangent line with negative slope, f′(x)<0. Where f(x) has a horizontal tangent line, f′(x)=0. If a function is differentiable at a point, then it is continuous at that point.

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