Determine the x-coordinates and find the intervals on which f is increasing and decreasing

Question

Let f(x)=4x^3+5. Find the open intervals on which f is increasing (Decreasing). Then determine the x-coordinates of all relative maxima and minima 

1. f is increasing on which interval?

2. f is decreasing on which interval?

3. The relative maxima of f occurs at x=

4. The relative minima of f occurs at x= 

 

Please provide final answers. 

Answer 1

To find increasing or decreasing find the first derivative and solve for zero. So in this case that's 12x^2 meaning we look around zero (-1 and 1). A parabola like this decreases until zero and increases after zero.

 

To find relative maxima and minima take the second derivative for 24x. Then x is still zero. it's negative going toward zero and positive going away from zero so relative minima is at zero.

 

Hope that helps,

Deanna