Relative Extrema Problem

[Jason76]

POST EDITED

\(\displaystyle g(20)= 0\)

\(\displaystyle g'(t)> 0\) for all values of \(\displaystyle t\)

The function \(\displaystyle g\) is differentiable on and satisfies the conditions above. Let F be the function given by \(\displaystyle F(x) = \int^{x}_{0} g(t) dt\) Which of the following be true?

Answer: \(\displaystyle F\) has a local minimum at \(\displaystyle x = 20\) Answer hints

 

[Bob Brown MSEE]

\(\displaystyle g(20)= 0\)

\(\displaystyle g'(t)< 0\) for all values of \(\displaystyle t\)

The function \(\displaystyle g\) is differentiable on and satisfies the conditions above. Let F be the function given by \(\displaystyle F(x) = \int^{x}_{0} g(t) dt\) Which of the following be true?

Answer: \(\displaystyle F\) has a local minimum at \(\displaystyle x = 20\) Answer hints

\(\displaystyle F\) has a local MAXIMUM at \(\displaystyle x = 20\)

 

[Jason76]

\(\displaystyle F\) has a local MAXIMUM at \(\displaystyle x = 20\)

Post Edited.

Typo

\(\displaystyle g'(t)> 0\) for all values of \(\displaystyle t\)

This is what is should say. But I had typed the opposite inequality sign.

 

[DrPhil]

POST EDITED

\(\displaystyle g(20)= 0\)

\(\displaystyle g'(t)> 0\) for all values of \(\displaystyle t\)

The function \(\displaystyle g\) is differentiable on and satisfies the conditions above. Let F be the function given by \(\displaystyle F(x) = \int^{x}_{0} g(t) dt\) Which of the following be true?

Answer: \(\displaystyle F\) has a local minimum at \(\displaystyle x = 20\) Answer hints

The hint is:

Use the Fundamental Theorem of Calculus