Question

Suppose that `f(x)= t^2 + 3t - 7`. What is the average rate of change of f (x) over the interval 5 to 6?

Answer 1

14

Explanation:

The average rate of change of a function is the same as the total change over the total time, i.e. the rate is

`bar(r) = (Deltaf(x))/(Deltax) = (f(6) - f(5))/(6-5) = f(6) - f(5) = 47 - 33 = 14`

Answer 2

`14`

Explanation:

`"the average rate of change is a measure of the slope of the"`
`color(blue)"secant line ""in the closed interval "[a,b]`

`"average rate of change "=(f(b)-f(a))/(b-a)`

`"here "[a,b]=[5,6]`

`f(b)=f(6)=36+18-7=47`

`f(a)=f(5)=25+15-7=33`

`rArr(47-33)/(6-5)=14`