Question

Find the slope and equation of the tangent line to the graph of the function at the given value of x.

f(x)=x^4-20x^2+64;x=-1

Answer 1

The slope is the differential of the function.

Recall, if y = x^n, (dy/dx) = nx^(n-1).

y=x^4-20x^2+64; x = -1. To differentiate this, we do it for each term.

(dy/dx) = (4)(x^(4 -1)) - (2)(20x^(2-1) + 0*64x^(0-1) (Note 64 = 64x^0, x^0 =1)
= (4)x^(3) - 40x^(1) + 0
= 4x^3 - 40x^1.

(dy/dx) = 4x^3 - 40x. Note at x = -1.


(dy/dx), x = -1, = 4(-1)^3 - 40(-1)
= -4 + 40 = 40 - 4 = 36.

Slope at x = -1 is 36.
Cheers.