A cubic polynomial function f is defined by f(x) = x^3 + ax^2 + b, where a and b are constants. This function has a stationary point at -1. Find a.

Question

butterflydreamer · Answer

Firstly we are given the function:
$$f(x) = x^3 + ax^2 + b $$

Now what do we know about stationary points? 
Stationary points occurs when $$f'(x) = 0$$ right?
So the first step is to differentiate f(x) to find f'(x)

anonymous · Answer

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

butterflydreamer · Answer

closeee but you forgot "a" .. Since "a" is a constant, when we differentiate ax^2, we get 2ax.
$$f(x) = x^3 + ax^2 + b$$
$$ f'(x) = 3x^2 + 2ax$$

To find stationary points, set f'(x) = 0
So therefore:
$$3x^2 + 2ax = 0$$
Factorise out the x 
x(3x + 2a) = 0
Note: x = 0 , -1 (since we're given one of the stationary points is -1)
This means that when 3x + 2a = 0, x = -1
Sub it in and solve for a :)!