Question

discuss the maximum and minimum value of the function defined as f(x)= sinx +cosx occuring in the interval [ 0,2π]​

Answer 1

Answer:

Step-by-step explanation:

y=sinx+cosx

= √2 [(1 / √2) sinx + cosx (1 / √2)]

= √2 [cos 45o sinx + cosx sin45o]

= √2 sin (x + 45o)

The minimum value of sinx is -1 and the minimum value of y is -√2.

Let the given function is f(x) that is f(x) = sinx +cosx

Finding the first derivative  

f'(x) = cosx - sinx

 

Equating it to zero

f'(x) =0

or, cosx - sinx =0

or, tanx =1  

or, x = 45 Degree

 

Finding the Second Derivative

f"(x) = -(sinx+cox)

At x= 45 , f"(x) <0

That means x = 45 is the point of maxima.

 

Hence the maximum value of the function f(x) is  

f(x= 45)

= sin 45 + cos 45

= Square Root 2  (Ans)

Answer 2

Answer:

There are 600 Toyota cars, parked in the airport road which is represented by an

angle of 50 degree. There are other cars named Audi, Nissan, Mazda parked in the

airport park.

How many Audi cars are there if there are represented by an angle of 85 degrees