Question

help?
Find the difference quotient and simplify your answer.

Answer 1

So it's asking for:
\[f(s) = -8s^2 - 7s\]
and it's giving you conditions for the variable s. Let's do the easier portion first.
\[f(3) = -8(3)^2 - 7(3) = -8(9) -21 = -72 -21 = -93\]

Answer 2

The part you probably had difficulty with looks like this:
\[f(3+h) = -8(3+h)^2 -(3+h)\]
Simplifying we get:
\[=-8(9+6h+h^2) -3-h\]
\[=-72 -48h -h^2 -3 - h = -h^2 -49h -75\]

Answer 3

Now just plug it in to the main equation
\[\frac{f(3+h)-f(3) }{h } = \frac{ -h^2-49h-75-93 }{h }\]
simplified:
\[\frac{ -h^2-49h-168 }{h } or \frac{ h^2+49h+168 }{ -h }\]

Answer 4

thank you!

Answer 5

Glad to help!