PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions for Mathematics

If f(x) attains a local minimum at x = c, then write the values of `f' (c)` and `f'' (c)`.

Write the minimum value of f(x) = \[x + \frac{1}{x}, x > 0 .\]

Write the maximum value of f(x) = \[x + \frac{1}{x}, x > 0 .\] 

Find the least value of f(x) = \[ax + \frac{b}{x}\], where a > 0, b > 0 and x > 0 .

Write the maximum value of f(x) = \[\frac{\log x}{x}\], if it exists .

The maximum value of x^1/x, x > 0 is __________ .

If \[ax + \frac{b}{x} \frac{>}{} c\] for all positive x where a,b,>0, then _______________ .

The minimum value of \[\frac{x}{\log_e x}\] is _____________ .

For the function f(x) = \[x + \frac{1}{x}\]

Let f(x) = x³+3x² \[-\] 9x+2. Then, f(x) has _________________ .

The minimum value of f(x) = \[x4 - x2 - 2x + 6\] is _____________ .

The number which exceeds its square by the greatest possible quantity is _________________ .

Let f(x) = (x \[-\] a)² + (x \[-\] b)² + (x \[-\] c)². Then, f(x) has a minimum at x = _____________ .

The sum of two non-zero numbers is 8, the minimum value of the sum of the reciprocals is ______________ .

The function f(x) = \[\sum^5_{r = 1}\] (x \[-\] r)² assumes minimum value at x = ______________ .