Question

Simply the difference quotient, tle="\frac{f(a+h)-f(a)}{h}" alt="\frac{f(a+h)-f(a)}{h}" align="absmiddle" class="latex-formula">, for $f(v)$=$-11v^2-8$
The difference quotient is ___

Answer 1

Greetings from Brasil...

F(V) = - 11V² - 8

F(a + h) - F(a)]/h

let's do it by steps

F(a + h) = - 11 · (a + h)² - 8

F(a + h) = - 11 · (a² + 2ah + h²) - 8

F(a + h) = - 11a² - 22ah - 11h² - 8

and

F(a) = - 11 · (a)² - 8

F(a) = - 11a² - 8

Then

F(a + h) - F(a)]/h

{- 11a² - 22ah - 11h² - 8 - [- 11a² - 8]}/h

[- 11a² - 22ah - 11h² - 8 + 11a² + 8]/h

[- 22ah - 11h²]/h

h · [- 22a - 11h]/h

[- 22a - 11h]