Find an equation of the tangent line to the curve at the given point. y = 6 x cos x, (pi , -6 pi)

Answer 1

Equation for a line is:

y-y1 = m(x-x1)

for f(x) = 6xcos(x), m = slope = f ' (x) = 6cos(x)-6xsin(x) by the product rule

at the point (pi, -6pi), m = 6cos(pi)-6(pi)sin(pi) = 6(-1) -6(pi)(0) = -6

substituting values into the slope intercept form of a line:

y-(-6pi) = -6(x-pi) -> y= -6x + 6pi -6pi -> y = -6x