Find the equation of the line that is tangent to the curve

Question

Find the equation of the line that is tangent to the curve

y = 6x cos x

at the point (π,−6π).

The equation of this tangent line can be written in the form y=mx+b

Answer 1

The find the equation of the line, you need to find the slope. This is done by taking the first derivative, using the product rule for this problem.

y' = 6x(-=sin x)+cos x (6) Now plug in x=π

y' = 6π(-=sin π)+cos π (6)

y' = 6π(0)+(-1)(6) = -6

m=-6

Now, I can plug my m, x and y values into the following equation

(y-y1)=m(x-x1)

(y-(-6π))=-6(x-π) Simplify

y+6π=-6x+6π Subtract 6π from both sides

y = -6x