take the derivitive
g'(x)=4x³-5
find whre it equals 0
4x³-5=0
4x³=5
x³=1.25
x=∛1.25≈1.08
make a sign chart
at 1.08, make a mark
evaluate the derivitive to the left and right of 1.08, make note of the sign only
g'(0)=(-)
g'(2)=(+)
the sign changes from negative to positive and is 0 at x=∛1.25
downward slope, then 0 slope then upward slope indicates a minimum
find the y value
g(∛1.25)=1.25∛1.25-5∛1.25+4≈-0.0395, rounded -0.04
minimum at (1.08,-0.04)