Question

5sinx+12cosx find the maximum value

Answer 1

root (5 square + 12 square)
= root (25+144)
= root 169
= 13

Answer 2

Maximum value of 5sinx+12cosx = 13

Step-by-step explanation:

f(x) = 5Sinx  + 12Cosx

Differentiating

f'(x) = 5Cosx - 12Sinx

putting f'(x) = 0

=>  5Cosx - 12Sinx = 0

=> 5Cosx = 12Sinx

=> tanx = 5/12

=> Sinx = 5/13  Cosx  = 12/13   or  Sinx = -5/13  Cosx  = -12/13

f''(x) = -5Sinx -12Cosx  = -ve   when  Sinx = 5/13  Cosx  = 12/13  

=> value is max when Sinx = 5/13  Cosx  = 12/13

5Sinx  + 12Cosx  

= 5(5/13)  + 12(12/13)

= 25/13 + 144/13

= 169/13

= 13

Maximum value of 5sinx+12cosx = 13

Minumum Value = 5(-5/13) + 12(-12/13)  = -169/13 = -13

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