Question

Find the equation of the line tangent to the function: f(x)=2cos(3x) at the point x0=pi/2.

Answer 1

The equation of the tangent is

y= 6x -3π

f(x) = 2cos(3x)

The slope of the tangent of the curve f(x) is equal to

f'(x) = dy/dx

f'(x) = -6sin(3x) at x= π/2

Slope = 6

At the point x = π/2 on the curve f(x) , the value of y = 2cos(3 × π/2)

y= 0

Point (π/2,0)

Slope of tangent = (y - y1)/(x - x1)

=> 6 = (y-0)/(x-π/2)

=> 6x -3π = y

=> y = 6x - 3π

The equation of the tangent touching the curve at (0, π/2) is

y= 6x- 3π