Question

Find by hand the intervals where the function is increasing and decreasing. Use this information to sketch a graph. y = x^4 - 8x^2 + 1

Answer 1

@bfsgd can u help?

Answer 2

$$\frac{dy}{dx} = 4x^3 - 16x = 4x(x^2 - 1)$$
We need this to be positive. Certainly positive for x>1 and that appears to be it.

Answer 3

That's for increasing.

Answer 4

It's decreasing where dy/dx <0 i.e. x<1 but not x=0.

Answer 5

or x=-1.

x=0,1,-1 are stationary points.

Answer 6

okay and how will the graph look like?