How do you find the equation of the line tangent to the graph of #y=2x*cos(x)# at the point #(pi, -2pi)#?

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Answer 1 · 2015-08-13T15:34:26

The equation in slope-intercept form is: #y = -2x#

#y=2x*cos(x)#

Find #y'# using the product rule:

#y' = 2cosx +2x(-sinx)#

# = 2cosx-2xsinx#

This is the formula for finding the slope of the tangent line.

At the point #(pi, -2pi)#, we find that the slope of the tangent line is

#2cosx-2xsinx]_(x=pi) = 2cos(pi)-2(pi)sin(pi)#

# = 2(-1)-2(pi)(0) = -2#

The equation of the line through #(pi, -2pi)# with slope #m=-2# is:

#y+2pi = -2(x-pi)" "#

Which can be written more simply as :

#y = -2x#

If you want the standard form, use:

#2x+y=0#