`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.

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1 Answer

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justaguide | College Teacher | (Level 2) Distinguished Educator

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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: