Question

Find the slope of the tangent using f(fx+h) - f(x) /h

y= x^3 at x =2

Answer 1

just plug into the formula and multiply out the cubic\[\frac{f(x+h)-f(x)}h=\frac{(x+h)^3-x^3}h=\frac{x^3+3x^2h+3xh^2+h^3-x^3}h\]\[=\frac{3x^2h+3xh^2+h^3}h=3x^2+3xh+h^2\]now you can take the limit as h approaches zero