Tangent line using basic differentation

Question

If , find .   Use this to find the equation of the tangent line to the curve  at the point . The equation of this tangent line can be written in the form  where  is: ​  and where  is:

Answer 1

Using the power rule, the derivative of h(x) = 4 − 3x³, is h'(x) = -9x² so h'(1) = -9 meaning the slope of the tangent line at (1, 1) is -9. That means the equation of the tangent line, using the point, slope form of a line is:

y - 1 = -9(x - 1)

y - 1 = -9x + 9

y = -9x + 10 so m = -9 and b = 10