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Application Of Derivatives

Question

Find the absolute maximum value and the absolute minimum value of the following functions in the given intervals:
$straight f left parenthesis straight x right parenthesis space equals space straight x cubed comma space space space straight x space element of space left square bracket negative 2 comma space space 2 right square bracket$

Solution

Here f (x) = x³The given function is differentiate for all x in [– 2, 2],
f ' (x) = 3x²Now f ' (x) = 0 ⇒ 3x² = 0 ⇒ x = 0 ∊ [– 2, 2]
f (0) = 0, f (– 2) = – 8, f (2) = 8
∴ absolute maximum value = 8 and absolute minimum value = – 8.

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.

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Application Of Derivatives

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.

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