Question

How do you find the relative extrema of the function `f (x)=x^4+4x^3+4x^2`?

Answer 1

You set the derivative to zero:

Explanation:

`f'(x)=4*x^3+3*4x^2+2*4x=0`

We can factorise:
`f'(x)=4x*(x^2+3x+2)=4x(x+1)(x+2)=0`
`->x=0orx=-1orx=-2`

Fill these in into the original function, and you'll get the coordinates:
graph{x^4+4x^3+4x^2 [-3.442, 2.717, -0.573, 2.503]}