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guru gati

VIEWS: 15 PAGES: 1

  • pg 1
									                                 GURU - GATI
                                          Class - xii
                                       (Increasing / decreasing)

Q1.    Show that the function f ( x)  x 2 is strictly increasing function on [0, ]
Q2.    Show that the function f ( x)  3x  12 is strictly decreasing on R.
                                                 1
Q3.    Show that the function f ( x)              is a decreasing function on (0, ).
                                                 x
Q4.    Without using the derivative, show that the function f(x)=|x| is
       (a) strictly increasing in (0, ).              (b) strictly decreasing in (-, 0).
Q5.    Find the intervals in which f ( x)  ( x  1) 3 ( x  3) 3 is increasing or decreasing.

                                            4x 2  1
Q6.    Find the intervals in which f ( x)           is increasing or decreasing.
                                               x
Q7.    Determine the intervals in which f ( x)  x 4  8 x 3  22 x 2  24 x  121 is
       increasing or decreasing.
                                                           x 2
Q8.    Determine the intervals in which f ( x)              ; x  0 is increasing or decreasing.
                                                           2 x
                                                                1
Q9.    Determine the intervals in which f ( x)  x 3              ; x  0 is increasing or
                                                                x3
       decreasing.
                                                                                                 1
Q10.   Let I be an interval disjointed from (-1, 1). Prove that the function f ( x)  x           is
                                                                                                 x
       increasing on I.
Q11.   Find the least value of a such that the function x 2  ax  1 is increasing on [1, 2].
Q12.   Find the values of k for which f ( x)  kx3  9kx2  9 x  3 is increasing on R.

Q13.   Show that f ( x)  e 2 x is increasing on R.
Q14.   Prove that the function f given by f(x) = x2 – x + 1 is neither increasing nor
       decreasing on (-1, 1).
Q15.   Find the intervals in which the following function is strictly increasing or strictly
       decreasing
       (a)      f ( x)  ( x  1) 3 ( x  3) 3

                            3 4 4 3          36
       (b)      f ( x)       x  x  3x 2     x  11
                           10    5           5

								
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