Find an example of a point (x,y) on the graph of f(x)=2cos(x) where the tangent...

Armorikam

Answered question

2021-02-09

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

Answer & Explanation

sovienesY

Skilled2021-02-10Added 89 answers

If u derivate the function f(x) u will have a function $[{f}^{\prime}(x)]$ 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)