Here is the problem (8b). I was asked to write out why the circled part was true.
I know that since the function is concave down then f"(x)<0. That is a fact. What I am having trouble with is why they can say the next part.
What I thought was L(x) is the tangent line and all tangent lines...
Attached is the problem and my work through the problem. I got the problem correct, but my teacher said this could be done quicker on a calculator. Any idea how it could be done quicker.
I did that. I let f(x)=sin. That way my overall function reads square root (sin(x^2)). I got that my final answer was 1/2(sin(x^2))^(-1/2) * -cos(x^2)*2x. Which does fit with my rule. Therefore that shows my answer is correct.
I started out by rewriting the function as (f(x^2))^(1/2). I then did chain rule to get 1/2(f(x^2))^(-1/2) *(f'(x^2).
- I think I need to go further because it is an x^2 in the function, but not sure.