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Write necessary condition for a point x = c to be an extreme point of the function f(x).
Concept: undefined >> undefined
Write sufficient conditions for a point x = c to be a point of local maximum.
Concept: undefined >> undefined
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If f(x) attains a local minimum at x = c, then write the values of `f' (c)` and `f'' (c)`.
Concept: undefined >> undefined
Write the minimum value of f(x) = \[x + \frac{1}{x}, x > 0 .\]
Concept: undefined >> undefined
Write the maximum value of f(x) = \[x + \frac{1}{x}, x > 0 .\]
Concept: undefined >> undefined
Write the point where f(x) = x log, x attains minimum value.
Concept: undefined >> undefined
Find the least value of f(x) = \[ax + \frac{b}{x}\], where a > 0, b > 0 and x > 0 .
Concept: undefined >> undefined
Write the minimum value of f(x) = xx .
Concept: undefined >> undefined
Write the maximum value of f(x) = x1/x.
Concept: undefined >> undefined
Write the maximum value of f(x) = \[\frac{\log x}{x}\], if it exists .
Concept: undefined >> undefined
The maximum value of x1/x, x > 0 is __________ .
Concept: undefined >> undefined
If \[ax + \frac{b}{x} \frac{>}{} c\] for all positive x where a,b,>0, then _______________ .
Concept: undefined >> undefined
The minimum value of \[\frac{x}{\log_e x}\] is _____________ .
Concept: undefined >> undefined
For the function f(x) = \[x + \frac{1}{x}\]
Concept: undefined >> undefined
Let f(x) = x3+3x2 \[-\] 9x+2. Then, f(x) has _________________ .
Concept: undefined >> undefined
The minimum value of f(x) = \[x4 - x2 - 2x + 6\] is _____________ .
Concept: undefined >> undefined
The number which exceeds its square by the greatest possible quantity is _________________ .
Concept: undefined >> undefined
Let f(x) = (x \[-\] a)2 + (x \[-\] b)2 + (x \[-\] c)2. Then, f(x) has a minimum at x = _____________ .
Concept: undefined >> undefined
The sum of two non-zero numbers is 8, the minimum value of the sum of the reciprocals is ______________ .
Concept: undefined >> undefined
The function f(x) = \[\sum^5_{r = 1}\] (x \[-\] r)2 assumes minimum value at x = ______________ .
Concept: undefined >> undefined
