Hi. If by second derivative test, if x = a is a critical point of f(x) and f''(a) > 0, then (a, f(a)) is a point of local minimum. Can you explain why my answer is wrong?Thank you so much! The graph of f"(x), the second derivative of f, is shown below. If the point (4, f(4)) is a critical number for f(x), is it alocal min, local max or neither?y =f"(x)6 -5 -4 -3 -2 -11 2 3 4/5 6 7a) O Neitherb) O Local minimumc)Local maximum

Answered: Image /qna-images/answer/dd136011-99ef-4fc1-b18e-52324c084afa.jpg

The graph of f"(x), the second derivative of f, is shown below. If the point (4, f(4)) is a critical number for f(x), is it a local min, local max or neither? y =f"(x) 6 -5 -4 -3 -2 -1 1 2 3 4/5 6 7 a) O Neither b) O Local minimum c) Local maximum

The graph of f"(x), the second derivative of f, is shown below. If the point (4, f(4)) is a critical number for f(x), is it a local min, local max or neither? y =f"(x) 6 -5 -4 -3 -2 -1 1 2 3 4/5 6 7 a) O Neither b) O Local minimum c) Local maximum

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter4: Polynomial And Rational Functions

Section4.2: Polynomial Functions

Problem 96E: What is the purpose of the Intermediate Value Theorem?

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Question

Hi. If by second derivative test, if x = a is a critical point of f(x) and f''(a) > 0, then (a, f(a)) is a point of local minimum. Can you explain why my answer is wrong?

Thank you so much!

The graph of f"(x), the second derivative of f, is shown below. If the point (4, f(4)) is a critical number for f(x), is it a
local min, local max or neither?
y =f"(x)
6 -5 -4 -3 -2 -1
1 2 3 4/5 6 7
a) O Neither
b) O Local minimum
c)
Local maximum

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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