Question

The derivative of f(x)=(x^4/3)-(x^5/5) attains its maximum at x= ?

Answer 1

the derivative of (x^4/3)-(x^5/5) is 4x³/3-1/5(5x^4)
make 4x³/3-1/5(5x^4)=0
x = 0 or x = 4/3
the derivative of the derivative of the function is -4(x-1)x²
now just use 0 and 4/3 at this function -4(x-1)x²
0 and -64/27
the point 4/3 refers to the function maximum value for x