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# HOW TO FIND THE MAXIMA AND THE MINIMA OF A FUNCTION. PLZ EXPLAIN WITH AN EXAMPLE.

Jitender Singh IIT Delhi
7 years ago
Ans:
Steps:
• First find the 1stderivative of a function.
• Equate 1stderivative to zero & find the roots of equation.
• Then calculate the value of 2nd derivative at roots of equation.
• If value of 2nd derivative is -ve, then that root is the maxima & if it is +ve, then root is the the minima.
Example:f(x) = sin(x)
Find maxima & minima of f(x) in interval 0 to 2 pi.
$f^{'}(x) = cos(x)$
$f^{'}(x) = 0$
$cos(x) = 0$
$x = \frac{\pi }{2}, \frac{3\pi }{2}$
$f^{''}(x) = -sin(x)$
$f^{''}(\frac{\pi }{2}) = -sin(\frac{\pi }{2}) = -1\rightarrow maxima$
$f^{''}(\frac{3\pi }{2}) = -sin(\frac{3\pi }{2}) = 1 \rightarrow minima$
$f(\frac{\pi }{2}) = sin(\frac{\pi }{2}) = 1\rightarrow maximum$
$f(\frac{3\pi }{2}) = sin(\frac{3\pi }{2}) = -1\rightarrow minimum$
Thanks & Regards
Jitender Singh
IIT Delhi