Question

Given p(u)= -2u^2 + 4u + 8, find the average rate of change of p over the interval [-7,4]

Answer 1

To get the average rate of change between two points of a function, we use the formula:

$\frac{p(u_2)-p(u_1)}{u_2-u_1}$

In this case, we have:

$\frac{p(4)-p(-7)}{4-(-7)}=\frac{p(4)-p(-7)}{11}$

Let's calculate p(4) and p(-7):

$p(4)=-2(4)^2+4\cdot4+8=-2\cdot16+16+8=-32+16+8=-8$$p(-7)=-2\cdot(-7)^2+4\cdot(-7)+8=-2\cdot49-28+8=-98-28+8=-118$

Now let's complete the calculation for the average:

$\frac{p(4)-p(-7)}{11}=\frac{-8-(-118)}{11}=\frac{110}{11}=10$

So, the answer is 10.