Question

How do you find all critical point and determine the min, max and inflection given `f(x)=x^2-8x-10`?

Answer 1

At `x=4` is a minimum only

Explanation:

`f(x)=x^2-8x-10`
Differentiating with respect to x, `f'(x)=2x-8`
Differentiating once more, `f''(x)=2` which is `>0` so we are expecting a minimum
When `f'(x)=0 => 2x-8=0 =>x=4`
When `x<4, f'(x) <0`
and when `x>4, f'(x)>0`
So we have a minimum
Check
`f(3)=3*3-8*3-10=-25`
`f(5)=5*5-8*5-10 =-25`
and `f(4)=4*4-8*4-10=-26`
So we have a min. only