Question

Let F be the function defined by F(X)=12X to the 2/3 power minus 4X Find the intervals of which F is increasing? Find X & Y coordinates of all relative max. pts? Find X and Y Coordinates of all relative min pts? Find the intervals of which F is concave down? Sketch a graph of F

Answer 1

I read your statement as
f(x) = 12x^(2/3) - 4x
then
f '(x) = 8x^(-1/3) - 4
= 0 for max/min

8/x^(1/3) = 4
4x^(1/3) = 8
x^(1/3) = 2
x = 8
then f(8) = 12(8)^(2/3) - 4(8)
= 48 - 32
= 16

Can you take it from here?

remember that the function is concave up when the second derivative is positive and
concave down .....

Answer 2

When the second derivative is negative