Question

Find the slope of the line tangent to the curve 3x2y+cosy=3√+π2 at the point (−1,π6) . (1 point) Responses −2π+6 − 2 π + 6 52π 5 2 π −2π5 − 2 π 5 2π5 2 π 5 −2π−6

Answer 1

To find the slope of the line tangent to the curve at the point (-1, π/6), we need to differentiate the given equation implicitly.

Taking the derivative of each term with respect to x, we get:
6xy + 3x(dy/dx) - sin(y)(dy/dx) = 0

Now, we substitute the given point (-1, π/6) into the equation and solve for dy/dx:
6(-1)(π/6) + 3(-1)(dy/dx) - sin(π/6)(dy/dx) = 0
-π + 3(dy/dx) - (1/2)(dy/dx) = 0
-π + (5/2)(dy/dx) = 0
(5/2)(dy/dx) = π
dy/dx = π/(5/2)
dy/dx = 2π/5

Therefore, the slope of the line tangent to the curve at the point (-1, π/6) is 2π/5.