Question

Find all critical numbers of f and classify the extreme values given x ∈ [0,12] and f(x)=x^2-22x+7.

Answer 1

f'(x)=2x-22
f'(x)=2(x-11)
critical numbers: x=11

Answer 2

Well firstly you gotta find the derivative of f(x)

Answer 3

What's my next move here? I'm stuck.

Answer 4

Right, which is 2(x-11)

Answer 5

Oh, and problem correction. It is x^2-22x+7

Answer 6

So the critical numbers are found using the first derivative, right? I get x=11 as the only critical number.

Answer 7

And the second derivative test gives the local min/max of that point. The second derivative in this case is only 2. Is it better to use a slope chart in this case?

Answer 8

wait just trying to remember how I use to solve this give me a sec

Answer 9

Well when f'(x)=0 its either a max or a min correct?

Answer 10

Yes, I think so. You find the first derivative, set it equal to zero, and then solve to find the critical numbers.

Answer 11

So what I tend to do was just plug in a 11 back into the original equation and you will right away know if its the min or the max

Answer 12

I found, using a slope chart, that 11 is a local min.

Answer 13

in this case its a parabola so its simple to know the shape