calculus
posted by adam .
A cubic polynomial function f is defined by
f(x)= 4x^3+ab^2+bx+k
where a, b, k, are constants. The function f has a local minimum at x=2
A. Fine the vales of a and b
B. If you integrate f(x) dx =32 from o to 1, what is the value of K?

I assume you typed the question wrong and meant f(x)= 4x^3 +ax^2 +bx+ k
The derivative f'(x) must be zero at x = 2, so
12x^2 + 2ax + b = 0 at x=2
48 4a +b = 0
You need more information to be able to calculate both a and b.