What is the maximum possible value of (21 Sin X + 72 Cos X)?
Explanation:
Let f (X) = 21 sin X + 72 cos X
∴ f ’(X) = 21 cos X – 72 sin X
At f ’(X) = 0
21 cos X = 72 sin X
∴ tan X = 2172
Drawing the corresponding right triangle we have the following:
∴ f ‘’(X) = –21 sin X – 72 cos X
= - 21 × 725 - 72 × 2425 < 0
∴ f (X) has a maximum at f ’(X) = 0
∴ Maximum value of f(x) = 21 × 2175 + 72 × 7275 = 75
Hence, option (d).
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