1 Answer | Add Yours
Find the critical value(s) by setting the first derivative equal to zero and solving for the x value(s).
Because 2=0 is not a true statement the first derivative will not produce a critical value.
If f'(x)>0 the function will increase in the interval.
If f'(x)<0 the function will decrease in the interval.
Notice f'(x)=undefined. This means the function is not differentiable at x=0.
Choose a value for x that is less than zero.
f'(-1)=-2/3 Since f'(-1)<0 the function is decreasing on the interval (-`oo,0).`
Choose a value for x that is greater than zero.
f'(1)=2/3 Since f'(1)>0 the function is increasing on the interval (0, `oo).`
Because the function changes direction from decreasing to increasing a relative minimum exists. The relative minimum exists at the point (0, -4) even though the derivative does not exist at that point.
We’ve answered 318,915 questions. We can answer yours, too.Ask a question