What is the local minimum value of the function? (round answer to the nearest hundredth)

g (x) = x^4-5x+4

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)