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Find the point of local maximum or local minimum, if any, of the following function, using the first derivative test. Also, find the local maximum or local minimum value, as the case may be: - Mathematics

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प्रश्न

Find the point of local maximum or local minimum, if any, of the following function, using the first derivative test. Also, find the local maximum or local minimum value, as the case may be:

f(x) = x3(2x \[-\] 1)3.

योग
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उत्तर

We have, f(x) = x3(2x − 1)3

Differentiate w..r.t x, we get,

f'(x) = 3x2(2x − 1)3 + 3x3(2x − 1)2·2

= 3x2(2x − 1)2(2x − 1 + 2x)

= 3x2(4x − 1)

For the point of local maxima and minima,

f'(x) = 0

= 3x2(4x − 1) = 0

= x = 0, `1/4`

At x = 1/4 f'(x) changes from −ve to + ve

Since, x = `1/4` is a point of minima

Hence, local min value f`(1/4) = -1/512`

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अध्याय 18: Maxima and Minima - Exercise 18.2 [पृष्ठ १६]

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आरडी शर्मा Mathematics [English] Class 12
अध्याय 18 Maxima and Minima
Exercise 18.2 | Q 13 | पृष्ठ १६

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