`f(x) = sin(2x), (pi,0)` (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...

`f(x) = sin(2x), (pi,0)` (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 f(x) = sin(2x). The slope of a line tangent to this curve at the point (pi,0) is given by the equation `(y - 0)/(x - pi) = f'(pi)`

`f'(x)= (sin (2x))'`

= 2*cos(2x)

`f'(pi) = 2`

This gives the equation of the required tangent: `y/(x - pi) = 2`

`y = 2*(x - pi)`

The graph of the function and the tangent is: