Question

Find the maximum value of 3 – 2 cos X

Answer 1

This is not the only way, if you explain the question, and then the asker tells you "but what's the answer?" or something along this line, then you know ....

Answer 2

Anyway.... if I were to deal with a triangle it would be less than five....

Answer 3

how cosx =1 and 2cosx =2

Answer 4

I mean cos(X)=-1
2cos(X)= -2
3-(-2) = 3+2=5

Answer 5

:find the absolute min and max values of f(x)= 2Cosx + Sin2x on the interval [0,pi/2]?

Solution : f(x)= 2Cosx + Sin2x

=>f'(x)=d/dx( 2Cosx + Sin2x)

=-2sinx+2cos2x

now,f'(x)=0

=> -2sinx+2cos2x=0

=>-2sinx+2(1-2sin^2x)=0 [cos2x= 1-2sin^2x]

=> -2sinx+2-4sin^2x+2=0

=> 4sin^2x+2sinx-2=0

=>4sin^2x+4sinx-2sinx-2=0

=> 4sinx(sinx+1)-2(sinx+1)=0

=>(4sinx-2)(sinx+1)=0

=> 4sinx=2 or sinx=-1 [condition not applicable for -ve ]

=>sinx=1/2=>x=π/6

Now, f(0)=2cos(0)+sin(2*0)

=2*1+0

=2

f(π/6)= 2cos(π/6)+sin(2*π/6)

= 2.√3/2+√3/2

= √3+√3/2

=( 2√3+√3)/2

=3√3/2

f(π/2)= 2cos(π/2)+sin(2*π/2)

= 2*0+0=0

Maximum value 3√3/2,at x=π/6

Minimum value 0 ,at x=π/2

Answer 6

kk

Answer 7

No, it is shifted 3 units up .

Answer 8

yeah, don't leave that out :)

Answer 9

I am going to post some shift rules on a different example.

\(\large\color{ blue }{\large {\bbox[5pt, lightyellow ,border:2px solid white ]{ \large\text{ }\\
\begin{array}{|c|c|c|c|}
\hline~~~~~~~~~~~~~~~~~~~~~~~~~~~\textbf{Shifts}~~~~~~~~~~~~~~~~~~~~~~~~~~~&~\bf{c~~~units~~~~} \\
\hline
\\f(x)= ∜x ~~~ ⇒ ~~~ f(x)= \sqrt[4]{x \normalsize\color{red }{ -~\rm{c}} } &~\rm{to~~the~~right~} \\
\text{ } \\
f(x)= ∜x ~~~ ⇒ ~~~ f(x)= \sqrt[4]{x \normalsize\color{red}{ +~\rm{c}} } &~\rm{to~~the~~left ~} \\
\text{ } \\
f(x)= ∜x ~~~ ⇒ ~~~ f(x)= ∜x \normalsize\color{red}{ +~\rm{c} } &~\rm{up~} \\
\text{ } \\
f(x)= ∜x ~~~ ⇒ ~~~ f(x)= ∜x \normalsize\color{red}{ -~\rm{c} } &~\rm{down~} \\ \\
\hline
\end{array} }}}\)

Answer 10

no need for desmos, but ty

Answer 11

my favorite graphing tool (after my paper and TI-84 calc)

Answer 12

oH yeah

Answer 13

I sometimes graph in the question if I have time....

Answer 14

idk shift rules and how to use it.and idk about graph

Answer 15

explain @SolomonZelman

Answer 16

wowee, this is not nearly so complicated i don't think

Answer 17

Find the maximum value of \(3 - 2 \cos(x)\)
the largest cosine can be is 1 and the smallest is -1
the biggest \(-2\cos(x)\) can be is \(2\)
the biggest \(3-2\cos(x)\) can be is \(3+2=5\)

Answer 18

yes I said that already, I was just giving an example of shifts ...