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

Question
Functions
asked 2020-11-06
Find an example of a point (x,y) on the graph of f(x)=2cos(x) where the tangent line has a slope of exactly 1.

Answers (1)

2020-11-07
If u derivate the function f(x) u will have a function [f'(x)] that will give u the slope for any value of x:
so, the derivate of the function \(f(x)=2cos(x) is f'(x) = -2sin(x)\), now to evalute where the derivate is equal to 1 (the slope that are asking for).
\(1 = -2 \sin(x) -> \sin^{-1} \frac{-1}{2} = \frac{-\pi}{6} = -0.53\)
So the x,y coordinate are (-0.53 , 1.72)
0

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