- #1

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## Homework Statement

##f(x)=12x^2-5##

The value of ##\lim_{h\rightarrow 0}\frac{f(x+2h)-f(x-3h)}{6h}## is ...

A. 8x

B. 10x

C. 12x

D.18x

E. 24x

## Homework Equations

##f'(x) = \lim_{h->0}\frac{f(x+h)-f(x))}{h}##

## The Attempt at a Solution

[/B]

Looking at the problem question, it seems that it's kinda like the definition of derivative

But, it's different.

This is my attempt.

##\lim_{h\rightarrow 0}\frac{f(x+2h)-f(x)}{2h}*\frac{2h}{6h}-\frac{f(x-3h)-f(x)}{3h}*\frac{3h}{6h}##

##= f'(x) * 1/3 - f'(x) * 1/2##

##= f'(x)*(-1/6)##

##= 24x (-1/6)##

##= -4x##

But, it's not in the options. Please help