Решите уравнение f``(x)=0 f(x)= ]cos^2 x/4-sin^2x/4. Created by Fanta76. matematika-ru

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Fanta76 @Fanta76

July 2022 1 7 Report

Решите уравнение f``(x)=0

f(x)= ]cos^2 x/4-sin^2x/4

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dtnth

Verified answer

$f(x)=cos^2 \frac{x}{4}-sin^2 \frac{x}{4}=cos(2*\frac{x}{4})=cos \frac{x}{2}$
$f'(x)=(cos \frac{x}{2})'=-sin \frac{x}{2}*\frac{1}{2}=-0.5sin \frac{x}{2}$
$f'(x)=0$
$-0.5sin \frac{x}{2}=0$
$\frac{x}{2}=\pi*k$
$x=2*\pi*k$
k є Z

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