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Find the Local Maxima and Local Minima, If Any, of the Following Functions. Find Also the Local Maximum and the Local Minimum Values, as the Case May Beg(X) = X3 − 3x - Mathematics

Find the local maxima and local minima, if any, of the following functions. Find also the local maximum and the local minimum values, as the case may be

g(x) = x3 − 3x

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Solution

g(x) = x3 − 3x

By second derivative test, = 1 is a point of local minima and local minimum value of g at x = 1 is g(1) = 13 − 3 = 1 − 3 = −2. However,

x = −1 is a point of local maxima and local maximum value of g at

x = −1 is g(1) = (−1)3 − 3 (− 1) = − 1 + 3 = 2.

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APPEARS IN

NCERT Class 12 Maths
Chapter 6 Application of Derivatives
Q 3.2 | Page 232
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