Let fx 65 sin x 67 cos x What is the maximum and minimum v

Let f(x) = 6.5 sin (x) + 6.7 cos (x). What is the maximum and minimum value of this function? Report answers accurate to 4 decimal places.

f(x) = 6.5 sin x + 6.7 cos x

find f\'(x) = 6.5cosx -6.7sinx

f\'(x) =0 ; 6.5cosx -6.7sinx =0

tanx = 6.5/6.7 = 0.97 ---> x = 44.13 ,

maximum / minium value occurs for x = 44.13 deg , 224.13

f(x) = 6.5(sin44.13) + 6.7(cos44.13) = 9.33

minimum value occurs when x=224.13 deg

f(x) = 6.5(sin224.13) + 6.7(cos224.13) = -9.33