Q. 3 - Calculus

Question

Identifying increasing and decreasing behavior: Use a graphing utility to determine the intervals on which $f\left(x\right)=-4x^5+25x^4-40x^3$is increasing or decreasing.

Step-by-Step Solution

Answer

The function $f\left(x\right)=-4x^5+25x^4-40x^3$is increasing on the interval $\left(2,3\right)$and decreasing on intervals $\left(-\infty ,2\right) \& \left(3,\infty \right).$

Step 1. Given information.

The given function is $f\left(x\right)=-4x^5+25x^4-40x^3.$

Step 2. Graph of function.

Plot the graph of function $f\left(x\right)=-4x^5+25x^4-40x^3$using a graphing utility.

The graph o function state that the function is increasing on the interval $(2,3)$and decreasing on intervals $\left(-\infty ,2\right) \& \left(3,\infty \right).$