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

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

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 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
askIITians Faculty

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