The derivative g' of a function g is continuous and has exactly two zeros. The second derivative g'" of a function g is continuous and has exactly one zero. Selected values of g, g' and g" are given in the table below. The domain of g is the set of all real numbers. -3 -1 1 2 4 g(x) g'(x) g"(x) -81 -7 -5 -16 -32 -25 63 15 -9 -12 15 -30 -18 12 -6 0. 12 18

The derivative g' of a function g is continuous and has exactly two zeros. The second derivative g'" of a function g is continuous and has exactly one zero. Selected values of g, g' and g" are given in the table below. The domain of g is the set of all real numbers. -3 -1 1 2 4 g(x) g'(x) g"(x) -81 -7 -5 -16 -32 -25 63 15 -9 -12 15 -30 -18 12 -6 0. 12 18

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.1: Polynomial Functions Of Degree Greater Than

Problem 35E

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Question

a) Evaluate integral from 5 to 1 of g'(x)dx. (problem also attached as a picture). Show your work.

b) What is the local minimum of g and where is it located? Justify your answer.

The derivative g' of a function g is continuous and has exactly two zeros. The second
derivative g'" of a function g is continuous and has exactly one zero. Selected values of g, g'
and g" are given in the table below. The domain of g is the set of all real numbers.
-3
-1
1
2
4
5
g(x)
g'(x)
g" (x)
-81
-7
-5
-16
-32
-25
63
15
-9
-12
15
-30
-18
12
-6
12
18

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 .

Expert Solution

Step 1 given question is:-

a) Evaluate integral from 5 to 1 of g'(x)dx. (problem also attached as a picture). Show your work.

b) What is the local minimum of g and where is it located? Justify your answer.

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