2 An increasing function is one whose gradient is always greater than or equal to zero. for all values of xA decreasing function has a gradient that is always negative or zero.for all values of x
3 e.g.1 Show that is an increasing function Solution:is the sum ofa positive number ( 3 ) a perfect square ( which is positive or zero for all values of x, anda positive number ( 4 )for all values of xso, is an increasing function
4 e.g.2 Show that is an increasing function. Solution:To show that is never negative ( in spite of the negative term ), we need to complete the square.for all values of xSince a square is always greater than or equal to zero,is an increasing function.