Question

The graph of f(x) = 2x + 1 is shown below. Explain how to find the average rate of change between x = 0 and x = 3. (10 points) Graph of 2 to the power of x plus 1 Courtesy of Texas Instruments

Answer 1

• f(x)=2x+1

We have to integrate the expression in order to find average rate of change.

$\boxed{\sf {\displaystyle{\int}}x^ndx=\dfrac{x^{n+1}}{n+1}}$

Now

$\\ \sf\longmapsto {\displaystyle{\int}^3_0}f(x)dx$

$\\ \sf\longmapsto {\displaystyle{\int}^3_0}(2x+1)dx$

$\\ \sf\longmapsto \left[\dfrac{2x^2}{2}+x\right]^3_0$

$\\ \sf\longmapsto [x^2+x]^3_0$

$\\ \sf\longmapsto 3^2+3-(0^2+0)$

$\\ \sf\longmapsto 9+3$

$\\ \sf\longmapsto 12$