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- https://math.libretexts.org/Courses/Coastline_College/Math_C180%3A_Calculus_I_(Nguyen)/04%3A_Applications_of_Derivatives/4.10%3A_Newtons_MethodIn many areas of pure and applied mathematics, we are interested in finding solutions to an equation of the form f(x)=0.f(x)=0. For most functions, however, it is difficult—if not impossible—to calc...In many areas of pure and applied mathematics, we are interested in finding solutions to an equation of the form f(x)=0.f(x)=0. For most functions, however, it is difficult—if not impossible—to calculate their zeroes explicitly. In this section, we take a look at a technique that provides a very efficient way of approximating the zeroes of functions. This technique makes use of tangent line approximations and is behind the method used often by calculators and computers to find zeroes.
- https://math.libretexts.org/Bookshelves/Calculus/Differential_Calculus_for_the_Life_Sciences_(Edelstein-Keshet)/05%3A_Tangent_lines_Linear_Approximation_and_Newtons_Method/5.04%3A_Tangent_Lines_for_Finding_Zeros_of_a_Function_-_Newtons_MethodIn many cases, it is impossible to compute a value of a zero, x∗ analytically. Based on tangent line approximations, we now explore Newton’s method, an approximation that does the job.
- https://math.libretexts.org/Courses/Mission_College/Math_3A%3A_Calculus_I_(Kravets)/04%3A_Applications_of_Derivatives/4.09%3A_Newtons_MethodIn many areas of pure and applied mathematics, we are interested in finding solutions to an equation of the form f(x)=0. For most functions, however, it is difficult—if not impossible—to calculate t...In many areas of pure and applied mathematics, we are interested in finding solutions to an equation of the form f(x)=0. For most functions, however, it is difficult—if not impossible—to calculate their zeroes explicitly. In this section, we take a look at a technique that provides a very efficient way of approximating the zeroes of functions. This technique makes use of tangent line approximations and is behind the method used often by calculators and computers to find zeroes.
- https://math.libretexts.org/Courses/Mission_College/Math_3A%3A_Calculus_I_(Reed)/04%3A_Applications_of_Derivatives/4.09%3A_Newtons_MethodIn many areas of pure and applied mathematics, we are interested in finding solutions to an equation of the form f(x)=0. For most functions, however, it is difficult—if not impossible—to calculate t...In many areas of pure and applied mathematics, we are interested in finding solutions to an equation of the form f(x)=0. For most functions, however, it is difficult—if not impossible—to calculate their zeroes explicitly. In this section, we take a look at a technique that provides a very efficient way of approximating the zeroes of functions. This technique makes use of tangent line approximations and is behind the method used often by calculators and computers to find zeroes.
- https://math.libretexts.org/Courses/Monroe_Community_College/MTH_210_Calculus_I_(Seeburger)/04%3A_Applications_of_Derivatives/4.09%3A_Newtons_MethodIn many areas of pure and applied mathematics, we are interested in finding solutions to an equation of the form f(x)=0.f(x)=0. For most functions, however, it is difficult—if not impossible—to calc...In many areas of pure and applied mathematics, we are interested in finding solutions to an equation of the form f(x)=0.f(x)=0. For most functions, however, it is difficult—if not impossible—to calculate their zeroes explicitly. In this section, we take a look at a technique that provides a very efficient way of approximating the zeroes of functions. This technique makes use of tangent line approximations and is behind the method used often by calculators and computers to find zeroes.
- https://math.libretexts.org/Courses/Prince_Georges_Community_College/MAT_2410%3A_Calculus_1_(Beck)/04%3A_Applications_of_Derivatives/4.10%3A_Newtons_MethodIn many areas of pure and applied mathematics, we are interested in finding solutions to an equation of the form f(x)=0. For most functions, however, it is difficult—if not impossible—to calculate t...In many areas of pure and applied mathematics, we are interested in finding solutions to an equation of the form f(x)=0. For most functions, however, it is difficult—if not impossible—to calculate their zeroes explicitly. In this section, we take a look at a technique that provides a very efficient way of approximating the zeroes of functions. This technique makes use of tangent line approximations and is behind the method used often by calculators and computers to find zeroes.
- https://math.libretexts.org/Bookshelves/Calculus/Differential_Calculus_for_the_Life_Sciences_(Edelstein-Keshet)/08%3A_Introducing_the_Chain_Rule/8.02%3A_The_chain_rule_applied_to_optimization_problemsArmed with the chain rule, we can now differentiate a wider variety of functions, and address problems that were not tractable with the power, product, or quotient rules alone. We return to optimizati...Armed with the chain rule, we can now differentiate a wider variety of functions, and address problems that were not tractable with the power, product, or quotient rules alone. We return to optimization problems where derivatives require use of the chain rule.
- https://math.libretexts.org/Courses/Laney_College/Math_3A%3A_Calculus_1_(Fall_2022)/04%3A_Applications_of_Derivatives/4.10%3A_Newtons_MethodIn many areas of pure and applied mathematics, we are interested in finding solutions to an equation of the form f(x)=0. For most functions, however, it is difficult—if not impossible—to calculate t...In many areas of pure and applied mathematics, we are interested in finding solutions to an equation of the form f(x)=0. For most functions, however, it is difficult—if not impossible—to calculate their zeroes explicitly. In this section, we take a look at a technique that provides a very efficient way of approximating the zeroes of functions. This technique makes use of tangent line approximations and is behind the method used often by calculators and computers to find zeroes.
- https://math.libretexts.org/Courses/City_College_of_San_Francisco/CCSF_Calculus/04%3A_Appropriate_Applications/4.07%3A_Newtons_MethodThis section covers Newton's Method, a technique for approximating roots of a function. Starting from an initial guess, the method iteratively applies the formula \( x_{n+1} = x_n - \frac{f(x_n)}{f'(x...This section covers Newton's Method, a technique for approximating roots of a function. Starting from an initial guess, the method iteratively applies the formula \( x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)} \) to get closer to the actual root. Examples illustrate how to use Newton's Method for finding solutions and demonstrate its effectiveness, especially when analytical solutions are challenging.
- https://math.libretexts.org/Courses/University_of_California_Davis/UCD_Mat_21A%3A_Differential_Calculus/4%3A_Applications_of_Definite_Integrals/4.7%3A_Newton's_MethodIn many areas of pure and applied mathematics, we are interested in finding solutions to an equation of the form f(x)=0. For most functions, however, it is difficult—if not impossible—to calculate th...In many areas of pure and applied mathematics, we are interested in finding solutions to an equation of the form f(x)=0. For most functions, however, it is difficult—if not impossible—to calculate their zeroes explicitly. In this section, we take a look at a technique that provides a very efficient way of approximating the zeroes of functions. This technique makes use of tangent line approximations and is behind the method used often by calculators and computers to find zeroes.
- https://math.libretexts.org/Courses/Coastline_College/Math_C180%3A_Calculus_I_(Everett)/04%3A_Applications_of_Derivatives/4.10%3A_Newtons_MethodIn many areas of pure and applied mathematics, we are interested in finding solutions to an equation of the form f(x)=0.f(x)=0. For most functions, however, it is difficult—if not impossible—to calc...In many areas of pure and applied mathematics, we are interested in finding solutions to an equation of the form f(x)=0.f(x)=0. For most functions, however, it is difficult—if not impossible—to calculate their zeroes explicitly. In this section, we take a look at a technique that provides a very efficient way of approximating the zeroes of functions. This technique makes use of tangent line approximations and is behind the method used often by calculators and computers to find zeroes.
