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# What is the slope of the tangent line to g(x)=cos(x+pi) at x=pi

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What is the slope of the tangent line to g(x)=cos(x+pi) at x=pi

Nov 27, 2018

#2
+18337
+2

This was answerd just a day or two ago:

remember    cos(x+pi) = -cos(x)

d/dx (-cos(x)) = sinx      and at pi    sin(x) = 0

Nov 27, 2018

#1
+5172
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The slope of the line tangent to a curve at a point is just the derivative of that curve evaluated at the point.

$$g(x) = \cos(x+\pi)\\ \dfrac{dg}{dx}(x) = -\sin(x+\pi)\\ \dfrac{dg}{dx}(\pi) = -\sin(\pi + \pi) = \\ \sin(2\pi) = 0\\ \text{hence the slope of the line tangent to }g(x) \text{ at }x=\pi \text{ equals }0.$$

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Nov 27, 2018
#2
+18337
+2

This was answerd just a day or two ago:

remember    cos(x+pi) = -cos(x)

d/dx (-cos(x)) = sinx      and at pi    sin(x) = 0

ElectricPavlov Nov 27, 2018