Question

Average rate of change:
h(x)= x^3 -0.5e^x at [0,1]

Answer 1

The 1/2 should be 1/3, sorry

Answer 2

If you mean that the 0.5 should be 1/3, then

h(x) = x^3 - 1/3 e^x
h(0) = -1/3
h(1) = 1 - e/3

so, avg rate of change is (h(1)-h(0))/(1-0) = 4/3 - e/3