Question

Use the first derivative to find all critical points and use the second derivative to find all the inflection points.

f(x)=2x^3+3x^2-36x+9

The critical point at x= _____
The critical point at x= _____

The inflection point is x= _____

Answer 1

I found:

f'(x) = 6x^2+6x-36
f"(x) = 12x+6

But I'm not sure what to do with f' since it can only be factored to 6(x^2+x-6)

The inflection point is x=-2, I think?
12x+6 = 0
12x = -6
x = -2

Answer 2

Oh yeah, duh. I would have figured that out once I plugged it in.
But I still need help with the critical points.

Answer 3

f'(x) = 6(x^2+x-6)
f'(x) = 6(x+3)(x-2)

To find critical points, set f'(x) = 0 and solve for x
6(x+3)(x-2) = 0
x = -3, +2 are critical points.

Answer 4

Point of inflection at x = -1/2.

Answer 5

Thanks!

Answer 6

you are welcome.