Question

Derivative help for calculus

Answer 1

I need to take the derivative of (x+2)^(2/3) +1

Answer 2

I have to solve for the critical numbers

Answer 3

f'(x)=(2/3)(x+2)^(-1/3)

Answer 4

I got stuck setting it to 0 and solving for the critical numbers

Answer 5

\[\Large\rm f'(x)=\frac{2}{3(x+2)^{1/3}}\]Mmm ok your derivative looks good.
So you also get critical numbers from the factors in the denominator.
They're just not the type of critical numbers you're thinking of.

Setting the derivative equal to zero,\[\Large\rm 0=\frac{2}{3(x+2)^{1/3}}\]The numerator tells us about any location where a horizontal tangent might be, and so, might lead us to max/min points.

The denominator is telling us where `vertical tangents` are located.
I dunno if these are always classified as critical points...

Answer 6

Yes, critical numbers are where f'(x)=0 or f'(x) is undefined

Answer 7

yes, you are right. I overlook it. Thanks :)