How do you find the point c in the interval #-4<=x<=6# such that f(c) is equation to the average value of #f(x)=2x#?

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Answer 1 · 2017-10-12T03:27:07

#1/(b-a) int_a^b f(x) dx#.

So we need to find the average value, then solve the equation #f(c) = "average value"# on the interval #[a,b]#.

For our case we get

Solve:

#2c = 1/(6-(-4)) int_-4^6 (2x) dx#

Evaluating the integral we get:

Solve: #2c = 2#.

The only solution is #c=1#