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Grade 12Algebra

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

Abhishek

12 Years agoGrade 12

1 Answer

Jitender Singh

12 Years ago

Ans:

Steps:

First find the 1^stderivative of a function.
Equate 1^stderivative to zero & find the roots of equation.
Then calculate the value of 2^nd derivative at roots of equation.
If value of 2^nd 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

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