Question

sinx + cosx how to find it is increasing or decreasing in interval (pi,pi)

Answer 1

Wherever dy/dx i positive, it is increasing .

Answer 2

i mean how, how to find critical point

Answer 3

sinx + cosx how to find the critical point:

1. find the derivative of f(x) = sinx + cosx
2. Set this derivative = to 0
3. solve for x on the interval [-Pi,Pi]

Answer 4

poo

Answer 5

poo

Answer 6

poo

Answer 7

poo

Answer 8

poo

Answer 9

Najeed: Ignore the spam. Just focus on your question and my replies.

Answer 10

sinx + cosx how to find the critical point:

1. find the derivative of f(x) = sinx + cosx
2. Set this derivative = to 0
3. solve for x on the interval [-Pi,Pi]

Answer 11

will you please elaborate it, and solve it for me please, i have a question like this "find incresing and decreasing of sinx -cosx {pi,pi}

Answer 12

@mathmale please

Answer 13

I'll do my best to guide you through the solution of this problem, but can't do the work for you.

Review: the derivative of sin x is cos x.
The derivative of cos x is - sin x.

What is the derivative of f(x) = sin x and cos x?

Answer 14

the derivative of sinx is cosx and cosx is -sinx

Answer 15

@mathmale

Answer 16

Good! Using that info, find the derivative of f(x) = sin x + cos x.

Answer 17

cosx-sinx

Answer 18

@mathmale

Answer 19

Fine. Now set that = to 0. How would you find the values of x that make the derivative = 0, on the interval [-Pi,Pi]?

Answer 20

something like this x=sin(inverse)*cosx

Answer 21

actually I am confused in finding the critical points for trignometric equations

Answer 22

@mathmale

Answer 23

There are a couple of different ways in which to solve equations such as f '(x) = cos x - sin x = 0.

One would be to graph each function (cos x and -sin x) on the same set of axes; you'd then look for the points at which the graphs intersect.

Another way would be to rewrite the equation: cos x - sin x = 0 as -sin x = -cos x, and then dividing both sides by cos x: \[\frac{ \sin x }{ \cos x }=1, ~ or ~\tan x=1.\] Solve for x.

Answer 24

amm then x will become x=tan(inverse)

Answer 25

At which angles between -Pi and +Pi is tan x = 1? Hint: these angles are in Q1 and Q3, but not in Q2 or Q4.

Answer 26

Try out your proposal. Decide whether you want your answer in degrees or in radians.

Answer 27

these angles will be tan 45 and tan 225 equals to 1

Answer 28

Yes indeed. That's it. Now you have the two critical values on [-Pi,Pi].

Answer 29

Now, how do you determine on which intervals the function is increasing and on which it is decreasing?

Answer 30

I will determine critical ponts by putting that value in derivative and if f'(x)<0 it will be decreasing and if x>0 then it will be increasing

Answer 31

@mathmale am I right??

Answer 32

Yes, that's basically right.
You need to set up intervals on the number line, like this: