`f(x) = (x - 6)^(2/3), c = 6` 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->6) (f(x) - f(c))/(x-c)`
`lim_(x->6) ((x-6)^(2/3))/(x-6)`
` `
Using division of exponents, it simplifies to:
`lim_(x->6) (x-6)^(-1/3) = 0`
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|, c = 6` Use the alternate form of the derivative to find the derivative at...
- 2 Educator Answers
- `f(x) = 3/x, c = 4` Use the alternate form of the derivative to find the derivative at x = c...
- 2 Educator Answers
- `f(x) = 1/(x+4), c=3` Use the alternative form of the derivative to find the derivative at x...
- 1 Educator Answer
gsarora17
| Certified Educator
calendarEducator since 2015
write762 answers
starTop subjects are Math, Science, and Business
`f(x)=(x-6)^(2/3)`
`f'(6)=lim_(h->0) (f(6+h)-f(6))/h`
`f'(6)=lim_(h->0) ((6+h-6)^(2/3)-(6-6)^(2/3))/h`
`f'(6)=lim_(h->0) h^(2/3)/h`
`f'(6)=lim_(h->0) h^(-1/3)`
`f'(6)=0`