Question

Find the equation of the tangent line to the curve y = 3x cos x at the point (pi, -3 pi). The equation of this tangent line can be written in the form y = mx + b. Compute m and b. m = b =

Answer 1

To find the equation of the tangent line to the curve y = 3x cos(x) at the point (pi, -3pi), find the derivative, plug in the x-coordinate, and use the point-slope form to find the equation.

Step-by-step explanation:

To find the equation of the tangent line to the curve y = 3x cos(x) at the point (pi, -3pi), we need to find the slope of the tangent line and the y-intercept.

Step 1: Find the derivative of the function

dy/dx = 3(cos(x) - x*sin(x))

Step 2: Plug in the x-coordinate of the given point

dy/dx = 3(cos(pi) - pi*sin(pi)) = 3(-1 - 0) = -3

Step 3: Use the point-slope form of a line to find the equation of the tangent line

y - y₁ = m(x - x₁)

y - (-3pi) = -3(x - pi)

y + 3pi = -3x + 3pi

y = -3x

So, the equation of the tangent line is y = -3x.