Page 19 - Math SL HB Sem 2

CI]RVE PROPERTIES

The derivative can be used to determine whether a firnction is increasing or
decreasing and so it can be used to hetp find those values of x for which the
function is increasing or decreasing.
v

-r

Ary tangent tine drawn in the Any tangeat line drawn in the Any tangent line &a*n in the
interval a < x< b will always interval b < x < c will always interval c < x < d will always
have a positive gradient This have a ocgarive gradient This have a positive gradient This

means that 4= f'(x'l> 0 meansthar f <O.O means that 4= f'(x\ > O
& fl= tl\
in this region. in this region. in this rcgion.

This means that to determine where a function is increasing or decreasing, the
values ofx for which f (x) > 0 and f 1x) < 0 respectively need to be found.

l9:

Find the values of x for which the function j(x) rlog. jE,r > 0 is increasing.
=

20:
values x the =l+4x- IS