Question

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

Answer 1

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

Answer 2

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

Answer 3

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.

Answer 4

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

Answer 5

\[f'(x)=1-(1/2)(9-x)^{1/2}\]

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

i meant =0?

Answer 10

\[(1/2)(9-x)^{1/2}=1\]

Answer 11

\[(9-x)^{1/2}=2\]

Answer 12

9-x=4
x=5