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

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.