Use the second derivative test to find the x-coordinates of all local minima given the following function g(x) = x³ − 4x² +10 If there are multiple values, give them separated by commas. If there are no local minima, enter Ø.

Use the second derivative test to find the x-coordinates of all local minima given the following function g(x) = x³ − 4x² +10 If there are multiple values, give them separated by commas. If there are no local minima, enter Ø.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.5: Rational Functions

Problem 51E

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Question

Use the second derivative test to find the x-coordinates of all local minima given the following function.

Formula Formula A function f ( x ) is also said to have attained a local minimum at x = a , if there exists a neighborhood ( a − δ , a + δ ) of a such that, f ( x ) > f ( a ) , ∀ x ∈ ( a − δ , a + δ ) , x ≠ a f ( x ) − f ( a ) > 0 , ∀ x ∈ ( a − δ , a + δ ) , x ≠ a In such a case f ( a ) is called the local minimum value of f ( x ) at x = a .

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