- #1

Kazane

- 5

- 0

## Homework Statement

f(x)=x

^{1/3}

use the definition of f'(a) to calculate the slope of the curve at x=1

(Hint: by rationalizing the numerator. useful formula a

^{3}-b

^{3}=(a-b)(a

^{2}+ab+b

^{2})

## The Attempt at a Solution

f'(x)=lim (x->1) f(x)-f(1)/x-1

=lim (x->1) x

^{1/3}-1

^{1/3}/ x-1

How can I do x

^{1/3}-1

^{1/3}to a

^{3}-b

^{3}=(a-b)(a

^{2}+ab+b

^{2})?

I'm confused so please help!