Find the derivative of this function?!?!SOMEONE HELP PLZ!!?

Question

lim h-->0, ((8+h)^2/3-4)/h
represents the derivative of a function f at point c. Determine f and c

Please explain how you got it

Sorry I meant to find out what f and c equals. Also, how do you solve this:
lim h->0, sin(h)/h what is f and c this time?????????

Answer 1

lim h-->0, ((8+h)^2/3-4)/h = f'(8) = f'(c), where f(x) = x^(2/3), and c = 8
f'(8) = (2/3)*8^(-1/3) = 1/3
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"lim h->0, sin(h)/h what is f and c this time?"
f(x) = sin(x), c = 0
f'(0) = -cos(0) = -1

Answer 2

I cannot understand your question. Your question says, "Find the derivative." Below, it says, "Determine f and c."
This may imply we need to integrate this function as the expression itself is the derivative.
Regardless, I have an answer. I am not sure of my answer.
This is 0/0 form. Use L'Hospital's Rule. Differentiate the numerator and the denominator.
lim h->0 (8+h)^2/3-4) /h
=lim h->0 (2/3)(8+h)^(-1/3) /1
=lim h->0 2 /3(8+h)^(1/3)=2/6 as h->0
=1/3
8^1/3=2

Answer 3

The function is f(x) = x^(2/3) and the point is c = 8.
To see this note that
the derivative of f(x) at a point a is
lim h-->0 ( f(a+h) - f(a))/h.
Here we clearly see that f(a+h) = (8+h)^(2/3)
and since 8^2/3 = f(a) = 4,
this gives the answer.

Answer 4

c = 8

f(x) = x^(2/3)
f'(x) = (2/3)/(cbrt x)

f(c) =8^(2/3)
f'(c) = (2/3)/2
f'(c) = 1/3