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

In order to get the maximum (or minimum) of a curve, we need to get the first derivative of the function or the slope then equate to zero. In order to confirm if the value of x is really the maxima, we can proceed to the second derivative and substitute the x to the equation. If the result is a negative number, then the point is the maxima. Therefore,

f(x) = (x^4/3) - (x^5/5)
f'(x) = (4x^3/3) - x^4 = 0

thus x = 4/3

check if the point is really the maxima

f"(x) = 4x^2 - 4x^3

substituting x = 4/3, we get an answer of -2.3704 thus the point is a maxima.