Another calculus question help please?

Question

(a) The point (2,8) is on the curve y=x^3, what is the gradient at this point?
(b) At what points on the curve does y=x^3 slope at 45 degrees?


please show me how to do this, thankjs

Answer 1

The derivative of a function is the slope of that function at every point.

f = x^3
f' = 3x^2

a) f'(2) = 12

b) 3x^2 = 1
x^2 = 1/3
x = sqrt(1/3)