Advadlippabrj

2022-01-27

Find the least value for $\mathrm{sin}x-{\mathrm{cos}}^{2}x-1$

At first I found the first derivative to be${y}^{\prime}=\mathrm{cos}x+2\mathrm{sin}x\mathrm{cos}x$

Critical point$0,-\frac{\pi}{6}$ (principal)

$y-\mathrm{sin}x+2\left(\mathrm{cos}2x\right)$

Then substitution of x by critical points I found minima. But my answer is incorrect.

Correct minimum value is$-\frac{9}{4}$

At first I found the first derivative to be

Critical point

Then substitution of x by critical points I found minima. But my answer is incorrect.

Correct minimum value is

Aiden Cooper

Beginner2022-01-28Added 14 answers

The equality occurs for

Micah May

Beginner2022-01-29Added 11 answers

Yes your way is correct indeed for $x=-\frac{\pi}{6}$ we have

$f\left(x\right)=-\frac{12}{-}\frac{34}{-}1=-\frac{94}{}$

As an alternative, recall that${\mathrm{cos}}^{2}x=1-{\mathrm{sin}}^{2}x$ and therefore we have

$f\left(x\right)=\mathrm{sin}x-{\mathrm{cos}}^{2}x-1={\mathrm{sin}}^{2}x+\mathrm{sin}x-2$

then set$t=\mathrm{sin}x$ and consider the parabola

$g\left(t\right)={t}^{2}+t-2\Rightarrow {g}^{\prime}\left(t\right)=2t+1=0\Rightarrow t=-\frac{1}{2}$

As an alternative, recall that

then set

Describe all solutions of Ax=0 in parametric vector form, where A is row equivalent to the given matrix

$$\left[\begin{array}{cccc}1& 3& 0& -4\\ 2& 6& 0& -8\end{array}\right]$$ Find, correct to the nearest degree, the three angles of the triangle with the given vertices

A(1, 0, -1), B(3, -2, 0), C(1, 3, 3)Whether f is a function from Z to R if

?

a) $f\left(n\right)=\pm n$.

b) $f\left(n\right)=\sqrt{{n}^{2}+1}$.

c) $f\left(n\right)=\frac{1}{{n}^{2}-4}$.How to write the expression ${6}^{\frac{3}{2}}$ in radical form?

How to evaluate $\mathrm{sin}\left(\frac{-5\pi}{4}\right)$?

What is the derivative of ${\mathrm{cot}}^{2}x$ ?

How to verify the identity: $\frac{\mathrm{cos}\left(x\right)-\mathrm{cos}\left(y\right)}{\mathrm{sin}\left(x\right)+\mathrm{sin}\left(y\right)}+\frac{\mathrm{sin}\left(x\right)-\mathrm{sin}\left(y\right)}{\mathrm{cos}\left(x\right)+\mathrm{cos}\left(y\right)}=0$?

Find $\mathrm{tan}\left(22.{5}^{\circ}\right)$ using the half-angle formula.

How to find the exact values of $\mathrm{cos}22.5\xb0$ using the half-angle formula?

How to express the complex number in trigonometric form: 5-5i?

The solution set of $\mathrm{tan}\theta =3\mathrm{cot}\theta $ is

How to find the angle between the vector and $x-$axis?

Find the probability of getting 5 Mondays in the month of february in a leap year.

How to find the inflection points for the given function $f\left(x\right)={x}^{3}-3{x}^{2}+6x$?

How do I find the value of sec(3pi/4)?