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प्रश्न
Examine the function f(x) = `x + 25/x ` for maxima and minima
उत्तर
f(x) = `x + 25/x`
`f'(x) = 1 - 25/x^2`
`f''(x) = 50/x^3`
f has maxima or minima if
f'(x) = 0
`1 - 25/x^2 = 0`
`x^2 - 25 = 0`
∴ x = 5 , x = -5
`f''(5) = 50/5^3`
`f''(5) = 2/5 > 0`
`f''(-5) = 50/(-5)^3`
`f''(-5) = (-2)/5 < 0`
∴ From equation (ii) f has maxima at x = - 5. And maximum value of f is
`f_(max) = f(-5)`
= `-5 + 25/-5`
= -10
Also from equation (i) f has minima at x = 5
And minimum value of f is
`f_(min) = f(5)`
= `5 + 25/5`
`f_(min) = 10`
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