`lim_(x->2) (f(x) - f(c))/(x-c)`

`lim_(x->2) (x^3 + 6x - 20)/(x-2)`

Simplify using synthetic division.

`lim_(x-> 2) x^2 + 2x + 10 = 18`

`f(x)=x^3+6x` ` `

`f'(2)=lim_(h->0) (f(2+h)-f(2))/h`

`f'(2)=lim_(h->0) (((2+h)^3+6(2+h))-(2^3+6*2))/h`

`f'(2)=lim_(h->0) ((2^3+h^3+6h(2+h)+12+6h)-(8+12))/h`

`f'(2)=lim_(h->0) (8+h^3+12h+6h^2+12+6h-20)/h`

`f'(2)=lim_(h->0) (h^3+6h^2+18h)/h`

`f'(2)=lim_(h->0) h^2+6h+18`

`f'(2)=18`

## We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support

Already a member? Log in here.

Are you a teacher? Sign up now