From first principles (ie using the tangent slope method), find the slope of the following curves at the given value of x.

Question

y=3x^3+1 at x=-4

Answer 1

f(x+h) - f(x) = (3(x+h)^3+1) - (3x^3-1) = 9x^2h +9xh^2 + 3h^3
Now divide that by h and take the limit as h→0 and you get
y' = 9x^2
now plug in x = -4

Answer 2

What do you mean by dividing with h?

Answer 3

he means
definition of derivative (slope at point x) is
[f(x+h) - f(x) ] / h
as h approaches zero