What is the equation of the tangent line of # f(x)=sinpix # at # x=3 #?

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Answer 1 · 2015-12-30T05:31:39

#y = pi(3-x)#

#color(blue)("Graph of "f(x))#
graph{sin(pix) [-10, 10, -5, 5]}

To construct a straight line, one needs either two points, or a point and the gradient. In this case, the latter would be more appropriate.

#f(3) = 0#

We know that the line passes through the point #(3,0)#.

#f'(x) = picospix#

#f'(3) = -pi#

We know that the gradient of the line is #-pi#.

#-pi = frac{y-0}{x-3}#

Equation of tangent line:

#y = pi(3-x)#

#color(blue)("Graph of tangent line")#
graph{pi(3-x) [-10, 10, -5, 5]}