Question

The maximum value of the function 4 cosx+3 sinx+20 *

25

27

30

45

​

Answer 1

Answer:

25

Step-by-step explanation:

y= 4cosx + 3sinx

y/5= sin(a+x)

where a= sin^-1 4/5

now maximum value if sin is 1

thus y/5 max = 1

y= 5

thus maximum value of the given function is 5+20

which is 25

Answer 2

Given :  4 cosx + 3 sinx + 20    

To Find : maximum value of the function

Solution:

f(x) = 4 cosx + 3 sinx + 20    

f'(x) = -4sinx + 3Cosx  

f'(x)  = 0

=>  -4sinx + 3Cosx  = 0

=> 4sinx  = 3cosx

=> tanx  = 3/4

Sinx  , cosx   = 3/5 , 4/5  respectively

or -3/5  , -4/5  respectively

f''(x)  =  -4cosx  - 3sinx  

Sinx  , cosx   = 3/5 , 4/5

=> f''(x)  < 0  hence maximum value  when  Sinx  = 3/5 , cosx  = 4/5  

f(x) = 4 cosx + 3 sinx + 20    

= 4(4/5) + 3(3/5) + 20

= 25/5 + 20

= 5 + 20

= 25

minimum value when   Sinx  = -3/5 , cosx  = -4/5  

= 4(-4/5) + 3(-3/5) + 20

= -5 + 20

= - 15

maximum Value = 25

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