Practice Problem 21

Question

Find an equation of the tangent line to the curve

at the point . Tangent line:

 

Answer 1

dy/dx= 3cos 3x - 8sin 8x

y(π/6)=-.5

derivative at (π/6,-.5) = 4√3

tangent line: 4√3 = (y+.5)/[x-(π/6)]

Answer 2

y' = 3cos(3x) - 8sin(8x). Slope of tangent line m = y'(π/6) = 3cos(π/2) - 8sin(4π/3) = 4√3;

y = sin(π/2) + cos(4π/3) = 1 - 1/2 = 1/2.

Equation of tangent line: y = 1/2 + 4√3(x - π/6)