if f(x)=3x^2-8x^-2 then lim as h approaches 0 f(2+h)-f(2)/h=

Question

anonymous · Answer

Thats the derivative of f at x = 2
f'(x) = 6x - 8
f'(2) = 4

It is 4.

ness9630 · Answer

Solve using the quotient rule right?

anonymous · Answer

It is not 4. It's a multiple choice question and my choices are: 10, 14, 20, -14, and -20.

campbell_st · Answer

you are being asked to use 1st princpals to find the derivative 

so this is tedious.... but do-able.. 

so substiute 2 + h into f(x) 

or

$$f(2 + h) = 3(2 + h)^2 - \frac{1}{(2 + h)^2} $$

and f(2) = 12 - 1/4 = 47/4

campbell_st · Answer

so you are looking at 

$$\lim_{h \rightarrow 0} \frac{(2 + h)^2 - \frac{1}{(2 + h)^2} - \frac{47}{4}}{h}$$

all you need to do now is simplify

campbell_st · Answer

good luck

anonymous · Answer

Thank you!

campbell_st · Answer

but I'm use the cheats method 

find $$f'(x) = 6x + \frac{16}{x^3}$$

then find 

f'(2) for the correct answer

campbell_st · Answer

oops 1'd not 1'm