Use the applet above to determine what you can say about the value of [math]c[/math] guaranteed by the Mean Value Theorem for Integrals if the function [math]f[/math] is linear.
If [math]f[/math] is linear, the value of [math]c[/math] guaranteed by the MVT for Integrals is given by [math]c=\frac{a+b}{2}[/math]. That is, [math]c[/math] is the average of, or the point exactly half way between, [math]a[/math] and [math]b[/math].