Application Of Derivatives

Question

Find all the local maxima or minima of the function
f (x) = x³– 12x.

Solution

Let f (x) = x³– 12 x
∴ f ' (x) =3 x² – 12
f ' ' (x) = 0 ⇒ 3 x²– 12 = 0 ⇒ x²– 4 = 0 ⇒ x = 2, – 2
f ' ' (x) = 6 x
At x = 2.
f ' ' (x) = 12 > 0
∴ f (x) has local minimum value at x = 2
and this minimum value = (2)³ – 12 (2) = – 16
At x = – 2, f ' ' (x) = – 12 < 0
∴ f (x) has local maximum value x = – 2
and this value = (– 2)³– 12 (– 2) = – 8 + 24 = 16.

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

Find all the local maxima or minima of the function
f (x) = x³– 12x.

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.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

Application Of Derivatives

Find all the local maxima or minima of the functionf (x) = x3 – 12x.

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.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Find all the local maxima or minima of the function
f (x) = x³– 12x.