Question

Determine where V(z)=z4(2z−8)3 is increasing and decreasing.

Answer 1

Answer and Explanation:

A function is said to be increasing, if the derivative of function is f’(x) > 0 on each point. A function is said to be decreasing if f”(x) < 0.

Let y = v (z) be differentiable on the interval (a, b). If two points z1 and z2 belongs to the interval (a, b) such that z1 < z2, then v (z1) ≤ v (z2), the function is increasing in this interval.

Similarly, the function y = v(z) is said to be decreasing, when it is differentiable on the interval (a , b).

Two points z1 and z2 Є (a, b) such that z1 > z2, then v (z1) ≥ v(z2). The function is decreasing on this interval.

The function y = v (z)

The derivative of function Y’ = v’(z) is positive, then the function is increasing.

The function y = v (z)  

The derivative of function y’ is negative, then the function is decreasing.