Question

Can someone help with derivatives?

Answer 1

Find the slope of the tangent line to the curve y=x^3 at the point (-1,-1)?

Answer 2

find the derivative of \(f(x)=x^3\) using the all mighty power rule
once you have \(f'(x)\) then compute \(f'(-1)\) for your answer

Answer 3

so use the equation \[\lim_{x \rightarrow -1}= (f(x)-f(a))\div(x-a)\]

Answer 4

ok we can do that too

Answer 5

\[\large \lim_{x\to -1}\frac{x^3+1}{x+1}\]

Answer 6

factor the numerator
it is the sum of two cubes
you get
\[\frac{(x+1)(x^2-x+1)}{x+1}\]

Answer 7

cancel, then replace \(x\) by \(-1\)

Answer 8

Thank you so much!