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# Write Sufficient Conditions for a Point X=C to Be a Point of Local Maximum. - CBSE (Arts) Class 12 - Mathematics

#### Question

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

#### 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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Solution Write Sufficient Conditions for a Point X=C to Be a Point of Local Maximum. Concept: Graph of Maxima and Minima.
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