Question

Find line tangent to y=xcosx at point (pi, -pi)

Answer 1

1) slope of the line = derivative of the of the function at the given point.

y' = cosx - x cosx

Evaluate for x = pi => y' = cos(pi) - pi*cos(pi) = -1 - (pi*cos(pi)) = -1 + pi

Then slope = -1 + pi

Given point: (pi, -pi)

Equation:

y - (-pi) = [-1+ pi] (x - pi)

y + pi = -x +pi + xpi -pi^2

y = (pi-1)x - pi^2      .... this is the answer