Question

Use the following graph of the function f(x) = −3x4 − x3 + 3x2 + x + 3 to answer this question: What is the average rate of change from x = 0 to x = 1?

Answer 1

the average rate of change is just the slope from (0,f(0)) to (1,f(1))

find f(0) and f(1)

$f(0)=-3(0)^4-(0)^3+3(0)^2+0+3=3$

$f(1)=-3(1)^4-(1)^3+3(1)^2+1+3=-3-1+3+1+3=3$

slope from (0,3) to (1,3) is rise/run=(3-3)/(0-1)=0/-1

the average rate of change from x=0 to x=1 for f(x) is 0