critical values

[Dorian Gray]

Hello Mathematicians,

I was wondering if somebody could please look over my work for this problem

(cubed root of x)(x+8)

My answer key says that the critical values are x=0 and x=8


I keep getting x=0 and x=-2 for my critical values.

 

[galactus]

You're correct, it is x = -2.

\(\displaystyle f(x)=\sqrt[3]{x}(x+8)\)

\(\displaystyle f'(x)=\frac{4(x+2)}{3\sqrt[3]{x^{2}}}\). Setting the numerator equal to 0 obviously results in x = -2.

There appears to be a discontinuity at x=0. See the x in the denominator?.

Since f(x) is defined at x=0, but f'(x) is not at x=0, it is a critical point as well.

 

[Dorian Gray]

thank you

Thank you Sir!

And I clearly see what you mean about the discontinuity with the x in the denominator of the derivative.