Question

How do you find the critical points for `f(x)= (2x^2+5x+5)/(x+1)`?

Answer 1

`(-2, -3), (0, 5)`

Explanation:

The derivative is either 0 or undefined:

`f'(x) = ((4x + 5)(x + 1) - 1(2x^2 + 5x + 5))/(x + 1)^2`
`f'(x) = (2x^2 + 4x)/(x + 1)^2`

`f'(x) = 0`
`(2x^2 + 4x)/(x + 1)^2=0`
`2x(x+2) = 0`
`x = -2, x = 0`

`f(-2) = -3`
`f(0) = 5`