Answer
a) $x\approx -2.28$
b) Maximum: $(-1,7)$;
Minimum: $(1,3)$
c) $(-\infty,-1)\cup(1,\infty)$
Work Step by Step
We are given the function:
$f(x)=x^3-3x+5$
a) Use a graphing utility to graph $f$:
There is a real zero:
$x\approx -2.28$
b) There is a local maximum:
$x_{max}\approx -1$
$y_{max}\approx 7$
There is a local minimum:
$x_{min}\approx 1$
$y_{min}\approx 3$
c) The function is increasing on the intervals:
$(-\infty,-1)\cup(1,\infty)$
