Find an equation of the tangent line to the graph of f(x) = (x3

Question

− 3x2 + 1)(2x4
− 1)
at x = −1.

Answer 1

f(x) = (x^3 − 3x^2 + 1)(2x^4 − 1)

using the product rule, ...
f ' (x) = (x^3 - 3x^2 + 1)(8x) + (2x^4 - 1)(3x^2 - 6x)

so f ' (-1) = (-1 - 3 + 1)(-8) + (2 - 1)(3 + 6)
= 24 + 9 = 33

f(-1) = (+1-3+1)(2-1) = -3

so you have the slope of 33 and a point (-1,-3)

y+3 = 33(x+1)
y = 33x + 30

Answer 2

thankyou!