Find the local maximum value of f using both the First and Second Derivative Tests.
f(x) = x + √9 - x

Question

anonymous · Answer

i already derivate the sqrt9-x to (9-x)^(1/2)

anonymous · Answer

but got stuck please shoe me steps but step to the answer so that way i can follow up

tad1 · Answer

If you wrote f(x) correctly, x + (-x) = 0 and f(x) become sqrt 9 which is a constant,  the derivative would be 0. By firts derivative test that would be a critical point. the 2nd derivative would also be 0, indicating a local max.

anonymous · Answer

I think he meant to say$$f(x)=x +\sqrt{9-x}$$right?

anonymous · Answer

$$f'(x)=1-(1/2)(9-x)^{1/2}$$

anonymous · Answer

yes im up to there now i need to solve it ....

anonymous · Answer

You set f'(x)=0 and solve for x. Let's see you try that.

anonymous · Answer

$$1-9/(2\sqrt{x})+0?$$

anonymous · Answer

i meant =0?

anonymous · Answer

$$(1/2)(9-x)^{1/2}=1$$

anonymous · Answer

$$(9-x)^{1/2}=2$$

anonymous · Answer

9-x=4
x=5