Question
Asked Sep 17, 2019
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f(x) = 10 cos x + 5 sin 2x
 
Determine the points in the interval (0, 2π) at which the graph of the function below has a horizontal tangent line.
 
-there should be 3 (x , y) values from smallest to largest x value 
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Expert Answer

Step 1

For finding the points on a function f(x), at which, f(x) has horizontal tangent line, we need to find all x, for which f’(x)=0.

Step 2

Lets find all the points of the given function on interval (0, 2π), for which f’(x)=0. So first calcutale f’(x).

f(x)10 cos r+5sin 2x
f'(x)10sin x + 10 cos 2.r 10(cos 2r- inr
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f(x)10 cos r+5sin 2x f'(x)10sin x + 10 cos 2.r 10(cos 2r- inr

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Step 3

Now solve for f&rs...

f x) 0
10(cos 2x -sinx)
0
cos 2x sin x 0
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f x) 0 10(cos 2x -sinx) 0 cos 2x sin x 0

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Tagged in

Math

Calculus

Functions