SOLUTION: Hi! A function is given below. Determine the average rate of change of the function between x = 0 and x = 0 + h. f(t) = &#8730;-3t thanks for your help!

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Question 198146: Hi!
A function is given below. Determine the average rate of change of the function between x = 0 and x = 0 + h.
f(t) = √-3t
thanks for your help!
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

First thing, you have expressed an interval of x = 0 to x = h, but your function is in terms of t. Either you want f(t) from t = 0 to t = h, or f(x) from x = 0 to x = h -- nothing else makes sense.

Furthermore, unless , this function is not defined over the reals because the domain of is and you have a coefficient of -3 on your independent variable. But assuming is the case, let's continue:

The average rate of change of a function over an interval is the slope of the secant line that passes through the two points on the function at the endpoints of the interval. So evaluate the function at each endpoint giving you two ordered pairs, in this case and .

The slope of the line passing through two points is given by:

so:

where

John

SOLUTION: Hi! A function is given below. Determine the average rate of change of the function between x = 0 and x = 0 + h. f(t) = &#8730;-3t thanks for your help!

SOLUTION: Hi! A function is given below. Determine the average rate of change of the function between x = 0 and x = 0 + h. f(t) = √-3t thanks for your help!