# Thread: Finding Max and Min

1. ## Finding Max and Min

Hi
Can someone show me how to find the max and min of the following equations without using the calculator:

1)$\displaystyle \frac{1}{2+sin(x)}$

i done $\displaystyle \frac{dy}{dx}$ and i got 1 however how do you get the minimum?

2)$\displaystyle \frac{1}{sin^2(x)+4}$

P.S

2. Originally Posted by Paymemoney
Hi
Can someone show me how to find the max and min of the following equations without using the calculator:

1)$\displaystyle \frac{1}{2+sin(x)}$

i done $\displaystyle \frac{dy}{dx}$ and i got 1 however how do you get the minimum?

2)$\displaystyle \frac{1}{sin^2(x)+4}$

P.S
Think about $\displaystyle \frac{1}{x}$ for $\displaystyle x > 0$.

The smaller $\displaystyle x$ gets, the bigger $\displaystyle \frac{1}{x}$ gets, and the bigger $\displaystyle x$ gets, the smaller $\displaystyle \frac{1}{x}$ gets.

So where is $\displaystyle 2 + \sin{x}$ at its minimum? This is where $\displaystyle \frac{1}{2 + \sin{x}}$ will be at its maximum.

Similarly, where is $\displaystyle 2 + \sin{x}$ at its maximum? This is where $\displaystyle \frac{1}{2 + \sin{x}}$ will be at its minimum.

Do the same for the second question.

3. We Will Do This :

$\displaystyle A = \frac {1}{2+\sin x}$

To Find Minimum -> Sinx=1 ( The Maximum of Sinx) So We Have :

$\displaystyle A = \frac {1}{2+1}=\frac {1}{3}$

To Find The Maximum - > Sinx=-1 { The Min of Sinx) So We Have:

$\displaystyle A = \frac {1}{2-1}= 1$

So

$\displaystyle \frac {1}{3} < A < 1$