Find the average rate of change of the function over the given interval. Compare this average rate of change with the instantaneous rates of change at the endpoints of the interval.

f(t) = 4t + 5, [1,2]

What is the average rate of change of the function g(t) over the interval from t = a to t = b? How is it related to a secant line?

Compare the average rate of change of the function over the given interval with the instantaneous rates of change at the endpoints of the interval. $g(x)=x^2+e^x,[0,1]$ 98, $h(x)=x^3-2 e^x, \quad[-1,0]$

Compare the average rate of change of the function over the given interval with the instantaneous rates of change at the endpoints of the interval.

$$h(x)=x^3-2 e^x, \quad[-1,0]$$

Find the average rate of change of the given function over the interval [a, a+h] for h=1, 0.01, and 0.001. (Round answers to four decimal places.) Then estimate the slope of the tangent line to the graph of the function at a. $f(x)=\frac{1}{x+1}$; a=0

Find the average rate of change of the function over the given interval. Compare this average rate of change with the instantaneous rates of change at the endpoints of the interval.

$$f(t)=4t+5, \quad [1,2]$$

Find the average rate of change of the function over the given interval. Compare this average rate of change with the instantaneous rates of change at the endpoints of the interval. f(t)=3t+5, [1, 2]

Find the average rate of change of the function over the given interval. Compare this average rate of change with the instantaneous rates of change at the endpoints of the interval. f(t)=t^2-7, [3,3.1]

How do the average rates of change for each pair of functions compare over the given interval? f(x) = -2x², g(x) = -4x², -4 ≤ x ≤ -2

A student calculates a function's average rate of change on an interval and finds that it is 0. The student concludes that the function is constant on the interval. Explain the students error, and give an example to support your explanation.

Which function has the greater average rate of change over the interval $-5 \leq x \leq 0$ :the translation of the function $f(x)=\sqrt[3]{x}$ to the right 1 unit and up 2 units, or the function $r(x)=\sqrt[3]{x}+3$ ?

On which interval is the average rate of change larger: [1, 2] or [2, 3]?

Find the average rate of change of the function over the given interval or intervals. h(t) = cot t

$$a.[ \pi / 4,3 \pi / 4 ] \quad \quad { b } . [ \pi / 6 , \pi / 2 ]$$

In following problem, find the average rate of change of the function over the given interval. Compare this average rate of change with the instantaneous rates of change at the endpoints of the interval.

$$h(x)=x^3-\frac{1}{2} e^x, \quad[0,2]$$