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

Question

1953 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-10-12T03:27:07

The average value of a function $f$ $f$ on interval $[a, b]$ $[a,b]$ is

$\frac{1}{b - a} \int_{a}^{b} f (x) d x$ $1/(b-a) int_a^b f(x) dx$ .

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

For our case we get

Solve:

$2 c = \frac{1}{6 - (- 4)} \int_{- 4}^{6} (2 x) d x$ $2c = 1/(6-(-4)) int_-4^6 (2x) dx$

Evaluating the integral we get:

Solve: $2 c = 2$ $2c = 2$ .

The only solution is $c = 1$ $c=1$

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