`y = cos(3x), ((pi/4),-sqrt(2)/2)` (a) Find an equation of the tangent line to the graph of f at the given point, (b) use a graphing utility to graph the function and its tangent line at the point,...

`y = cos(3x), ((pi/4),-sqrt(2)/2)` (a) Find an equation of the tangent line to the graph of f at the given point, (b) use a graphing utility to graph the function and its tangent line at the point, and (c) use the derivative feature of the graphing utility to confirm your results.

Expert Answers
justaguide eNotes educator| Certified Educator

The function y = cos (3x). The slope of the tangent to the graph of this function at `(pi/4, -sqrt2/2)` is `(y + sqrt 2/2)/(x - pi/4) = y'(pi/4)`

`y' = -3*sin(3*x)`

`y'(pi/4) = -3/sqrt 2`

The equation of the tangent is:

`(y + sqrt 2/2)/(x - pi/4) = -3/sqrt 2`

`y = (-3/sqrt 2)*(x - pi/4) + 1/sqrt 2`

The required equation of the tangent to the curve y = cos 3x at x = `pi/4` is `y = (-3/sqrt (2))*(x - pi/4) - 1/sqrt (2)`

The graph of the curve and the tangent is: