Functions: find a, b so f(x) = x^3+ax^2+b is....

[dme]

Hi Everyone,

Here is the question.

Find the values of the constants a and b such that the function f(x)= x^3 + ax^2+b
is increasing where x < 1, the function is decreasing where x > 1, and f(1) = 6.

Step 1: Find derivative

f'(x) = 3x^2 + 2ax

Step 2: Not too sure what comes next.

Could someone help when they have the chance?
Thanks!

 

[stapel]

You are given the value of f for x = 1. What equation does this give you?

You are given that (1, 6) is the maximum point. What does this allow you to conclude about the derivative at x = 1?

Eliz.