Q. 2 - Calculus

Question

Consider the graph of the function f shown next. Define A(x) to be the area of the region between the graph of f and the x-axis from 0 to x. We will count areas of regions above
the x-axis positively and areas of regions below the x-axis negatively.

From the graph of f , estimate all local maxima and minima of A(x).

Step-by-Step Solution

Answer

The local minimum of the function is at $x=0,5$ and the local maximum is at $x=3$.

Step 1. Given Information.

The graph.

Step 2. Find all local maxima and minima.

From the graph, the area of the function is,

$A\left(x\right)=\frac{12x^4}{4}-\frac{96x^3}{3}+\frac{180x^2}{2}$

From the graph, the local minimum of the function is at $x=0,5$ and the local maximum is at $x=3$.