Mathematics, 25.03.2020 14:38 20guadalupee73248

Y=4x-2tan(x), (-pi/2,pi/2)
which are the relative min and max?

Answers: 1

Show answers

Answers

Answer from: rleiphart1

relative max = pi -2

relative min = -2 pi

Step-by-step explanation:

y= 4x- 2tan(x), (-pi/2,pi/2)

To find relative max and min,

According to mathematical procedure to find relative max and relative min,

the following procedure should be carry out.

Derivating equation with respect to x,

$\frac{dy}{dx} =\frac{d}{dx} (4\times x -2 \times tan x)$ .....(1)

Equating equation (1) to Zero,

We get,

$0 =\frac{d}{dy} (4\times x -2 \times tan x)$

$0 = 4 -2 \times sec^{2} x$

$4 = 2 \times sec^{2} x$

$2 = sec^{2} x$

$x= \frac{\pi }{4}$ ....stationary point

There are total three points

1. -pi/2 2. pi/2 3. pi/4

checking local min and local max

first considering -pi/2;

$\frac{d^{2}y }{dx^{2} } =\frac{d^{2} }{dx^{2} } (4\times x -2 \times tan x)$ ...(2)

putting x= pi/4 in equation (2),

we get,

$\frac{d^{2}y }{dx^{2} } = -4$ <0

So, we have local max at x=pi/4

by putting value of x in equation (1);

we get,

$y = 4\times (\pi /4 ) -2 \times tan (\pi /4 )$

$y = \pi - 2$ .... is maximum point.

Similarly, at x= -pi/ 2,

$\frac{d^{2}y }{dx^{2} } = 1$ >0

So, we have local min at x=-pi/2

by putting value of x in equation (1);

we get,

$y = 4\times (-\pi /2 ) -2 \times tan (-\pi /2 )$

$y = -2 \times \pi$ .... is minimum point

Answer from: aeverettpdzrvo

The relative max & min is y=1.14 & y=-1.14 respectively .

Step-by-step explanation:

Here we have , y=4x-2tan(x) in interval (-pi/2,pi/2) . We need to find the relative min and max . Let's find out;

We will first differentiate this function with respect to x and then , we'll put it to zero to find values of x for which function is maximum & minimum .

y=4x-2tan(x) , Differentiating w.r.t x we get:

⇒ $\frac{d(y)}{dx}=\frac{d(4x-2tan(x))}{dx}$

⇒ $\frac{d(y)}{dx}=\frac{d(4x)-d(2tan(x))}{dx}$

⇒ $\frac{d(y)}{dx}={4-(2sec^2x)$ { $\frac{d(tanx)}{dx}=sec^2x$ }

Now, equation this to zero :

⇒ 4-(2sec^2x) = 0

⇒ 2sec^2x = 4

⇒ sec^2x = 2

⇒ $secx = \pm \sqrt{2}$

⇒ $x = sec^{-1}(\pm \sqrt{2})$

⇒ $x =(\pm \frac{\pi }{4} )$

Now , At x = $\frac{\pi}{4}$ :

⇒ y=4x-2tan(x)

⇒ $y=4(\frac{\pi }{4})-2tan(\frac{\pi }{4})$

⇒ $y=\pi-2(1)$

⇒ y=1.14

At x= - $\frac{\pi}{4}$ :

⇒ y=4x-2tan(x)

⇒ $y=4(\frac{-\pi }{4})-2tan(\frac{-\pi }{4})$

⇒ $y=-\pi-2(-1)$

⇒ y=-1.14

Therefore , The relative max & min is y=1.14 & y=-1.14 respectively .

Answer from: Quest

Sin(a)+cos(a)+cot(a)-1=2(csc(x)+1)

Answer from: Quest

i think the answer is true

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 15:30

After being rearranged and simplified, which of the following equations could be solved using the quadratic formula? check all that apply. a. 9% + 3x2 = 14 + x-1 b. -x+ + 4x + 7 = -32-9 c. 5x + 4 = 3x4 - 2 d. 2x2 + x2 + x = 30

Answers: 1

Answer

Mathematics, 21.06.2019 19:00

Quick! a survey of 57 customers was taken at a bookstore regarding the types of books purchased. the survey found that 33 customers purchased mysteries, 25 purchased science fiction, 18 purchased romance novels, 12 purchased mysteries and science fiction, 9 purchased mysteries and romance novels, 6 purchased science fiction and romance novels, and 2 purchased all three types of books. a) how many of the customers surveyed purchased only mysteries? b) how many purchased mysteries and science fiction, but not romance novels? c) how many purchased mysteries or science fiction? d) how many purchased mysteries or science fiction, but not romance novels? e) how many purchased exactly two types of books?

Answers: 3

Answer

Mathematics, 21.06.2019 20:30

Cody was 165cm tall on the first day of school this year, which was 10% taller than he was on the first day of school last year.

Answers: 1

Answer

Mathematics, 21.06.2019 21:30

About 9% of th population is hopelessly romantic. if 2 people are randomly selected from the population, what is the probability that at least 1 person is hopelessly romantic?