Armorikam

2021-02-09

Find an example of a point (x,y) on the graph of $f\left(x\right)=2\mathrm{cos}\left(x\right)$ where the tangent line has a slope of exactly 1.

sovienesY

If u derivate the function f(x) u will have a function $\left[{f}^{\prime }\left(x\right)\right]$ that will give u the slope for any value of x:
so, the derivate of the function $f\left(x\right)=2\mathrm{cos}\left(x\right)is{f}^{\prime }\left(x\right)=-2\mathrm{sin}\left(x\right)$, now to evalute where the derivate is equal to 1 (the slope that are asking for).
$1=-2\mathrm{sin}\left(x\right)\to {\mathrm{sin}}^{-1}\frac{-1}{2}=\frac{-\pi }{6}=-0.53$
So the x,y coordinate are (-0.53 , 1.72)

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