Question

f(x)=x¹/³(x+3)²/³ x ∈ R⁺,Find the maximum and minimum value of the given function.

Answer 1

Dear Student:

F(x)=x¹/³(x+3)²/³ x ∈ R⁺

For,maximum and minimum  

We will find $\frac{df}{dx}$ and then equate to zero.

And then again proceed for second derivative and see it is negative or positive.

If it is positive then f will be minimum

And if negative then f maximum

If it is zero then try to plot f and see whether there exist minimum or maximum or not.

In this range R+ there is no maximum and minimum.

See the attachment: