f(x) = x^4 - 40 x^3
For what values of x does the slope of the curve = 0?
At what value(s) of x does f have a local maximum or a local minimum?

Question

f(x) = x^4 - 40 x^3 
For what values of x does the slope of the curve = 0?
At what value(s) of x does f have a local maximum or a local minimum?

anonymous · Answer

Find the x-coordinates of all inflection points.

anonymous · Answer

Taking the derivative you get the function for the slope at a point x as $$4x^3 - 120x^2$$. Then setting that equal to zero and solving. $$4x^3 - 120x^2=0$$. $$4x^2(x - 30)=0$$. $$x=0$$ or $$x=30$$. At those two points the function has a slope of zero. The determine the local max or min, take the second derivative.$$x(8x - 240) $$

anonymous · Answer

so I would just plug in 0 and 30 into the equation x(8x-240) for x ?

anonymous · Answer

to find the max and min?