`f(x) = x^3 + 2x^2 + 1, c = -2` Use the alternate form of the derivative to find the derivative at x = c (if it exists)
- print Print
- list Cite
Expert Answers
leonard-chen
| Certified Educator
calendarEducator since 2015
write9 answers
starTop subject is Math
`lim_(x->-2) (f(x) - f(c))/(x-c)`
` ` `lim_(x->-2) (x^3 + 2x^2)/(x+2)`
Simplify using synthetic division.
` `
`lim_(x->-2) x^2 = 4`
Related Questions
- `f(x) = x^2 - 5, c = 3` Use the alternate form of the derivative to find the derivative at x...
- 2 Educator Answers
- `f(x) = x^3 + 6x, c = 2` Use the alternate form of the derivative to find the derivative at...
- 2 Educator Answers
- `f(x) = (x - 6)^(2/3), c = 6` Use the alternate form of the derivative to find the...
- 2 Educator Answers
- Find the derivative of fog(x) is f(x)= 2x-3 and g(x) = x^2-2
- 2 Educator Answers
- Find f'(c) for c = 2 and c = -1 forming the difference quotient f(x)= 2x + 3
- 1 Educator Answer
gsarora17
| Certified Educator
calendarEducator since 2015
write762 answers
starTop subjects are Math, Science, and Business
`f'(-2)=lim_(h->0) (f(-2+h)-f(-2))/h`
`f'(-2)=lim_(h->0) (((-2+h)^3+2(-2+h)^2+1) -((-2)^3+2(-2)^2+1))/h`
`f'(-2)=lim_(h->0) (((-2)^3+h^3+3(-2h)(-2+h)+2(4+h^2-4h)+1)-(-8+8+1))/h`
`f'(-2)=lim_(h->0) ((-8+h^3+12h-6h^2+8+2h^2-8h+1)-1)/h`
`f'(-2)=lim_(h->0) (h^3-4h^2+4h)/h`
`f'(-2)=lim_(h->0) h^2-4h+4`
`f'(-2)=4`