Thursday, January 21, 2016

Calculus: Early Transcendentals, Chapter 4, 4.9, Section 4.9, Problem 58

Graph of f can be seen in the picture below (blue line).
From this we can sketch graph of its antiderivative. We start drawing from left to right. As long as f is positive (graph above x-axis) antiderivative is increasing and it reaches maximum when f(x)=0. It continues to decrease until f reaches zero again (minimum of antiderivative). After that (right of that) graph of f lies above x-axis so the antiderivative is increasing.
Graph of antiderivative can be seen in the picture below (red line).

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