Question

the largest value of 5sin theta+9 is ___.​

Answer 1

Given :  5sinθ + 9

To Find : largest value  

Solution

5sinθ + 9

sinθ range is [-1 , 1]

maximum value of sinθ = 1

Hence 5sinθ + 9

= 5(1) + 9

= 14

Largest Value is 14

largest value of 5sinθ+9 is 14

f(θ) = 5sinθ + 9

f'(θ) = 5cosθ

5cosθ  = 0

=> θ = π/2 , 3π/2

f''(θ) = -5Sinθ

f''  (π/2) = -5Sinπ/2 = - 5 < 0  Hence maximum value at  π/2

f''  (3π/2) = -5Sin3π/2 = 5 > 0  Hence minimum value at  3π/2

f(π/2) = 5sinπ/2 + 9  = 5 + 9 = 14     largest value

f(3π/2) = 5sinπ/2 + 9  = -5 + 9 =  4   Smallest Value

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