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Write Sufficient Conditions for a Point X=C to Be a Point of Local Maximum. - Mathematics

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Question

Write sufficient conditions for a point x = c to be a point of local maximum.

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Sum
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Solution

We know that at the extreme points of a function f(x), the first order derivative of the function is equal to zero, i.e.
`f '(x) = 0 " at "x = c`

`⇒ f '(c) = 0`
Also, at the point of local maximum, the second order derivative of the function at the given point must be less than zero, i.e.
`f''(c) < 0`
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Chapter 18: Maxima and Minima - Exercise 18.6 [Page 80]

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RD Sharma Mathematics [English] Class 12
Chapter 18 Maxima and Minima
Exercise 18.6 | Q 2 | Page 80

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