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Application of Derivatives
Question
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Find the maximum or minimum values, if any, of the following functions without using the derivatives:
|sin 4x + 3|

Answer

Let f(x) = |sin 4x + 3|
∵   – 1 ≤ sin 4x ≤ 1 
∴ – 1 + 3 ≤ sin 4x + 3 ≤ 1 + 3
⇒  2 < sin 4x + 3 ≤ 4 ⇒ 2 ≤ | sin 4x + 3 | ≤ 4
⇒ 2 ≤ f (x) ≤ 4
∴  maximum value of f (x) is 4 and minimum value of f (x) is 2.

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Some More Questions From Application of Derivatives Chapter

The radius of a circle is increasing uniformly at the rate of 4 cm per second Find the rate at which the area of the circle is increasing when the radius is 8 cm.