Answered

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Let f(x) = cos(x) + 2x.
Where does f have critical points?

Sagot :

xKelvin

Answer:

f has no critical points.

Step-by-step explanation:

We are given:

[tex]f(x)=\cos(x)+2x[/tex]

A function has critical points whenever its derivative equals 0 or is undefined.

Differentiate the function:

[tex]f'(x)=-\sin(x)+2[/tex]

Since this will never be undefined, solve for its zeros:

[tex]0=-\sin(x)+2[/tex]

Hence:

[tex]\displaystyle \sin(x)=2[/tex]

Recall that the value of sine is always between -1 and 1.

Thus, no real solutions exist.

Therefore, f has no critical points.

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