Lucille Davidson

2022-01-16

Maximum and minimum of $f\left(x\right)=2{\mathrm{sin}}^{2}x+2{\mathrm{cos}}^{4}x$

Bertha Jordan

Beginner2022-01-17Added 37 answers

You also could linearise the function first, doing some trigonometry:

$2{\mathrm{sin}}^{2}x+2{\mathrm{cos}}^{4}x=1-\mathrm{cos}2x+{\frac{12}{2{\mathrm{cos}}^{2}x}}^{2}=$

$=1-\mathrm{cos}2x+\frac{12}{+}\mathrm{cos}2x+{\frac{12}{\mathrm{cos}}}^{2}2x$

$=\frac{32}{+}\frac{1+\mathrm{cos}4x}{4}=\frac{7+\mathrm{cos}4x}{4}$

Now it is obvious this expression has a global minimum when$\mathrm{cos}4x=-1$ and a global maximum when $\mathrm{cos}4x=1$

Now it is obvious this expression has a global minimum when

RizerMix

Expert2022-01-20Added 656 answers

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