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# Determine the average rate of change of the function between the given values of the variable.

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A function is given. Determine the average rate of change of the function between the given values of the variable.

f(t) =

f(t) = 7/t;    t = a, t = a + h
Jun 16, 2014

#8
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I suspect sally1 is expecting this to be taken just a little further, so taking up where Melody left off:

(f(a+h) - f(a))/h = (7/(a+h) - 7/a)/h

= (7a - 7(a+h))/(a*(a+h)*h)

= -7h/(a*(a+h)*h)

= -7/(a*(a+h))

Jun 17, 2014

#1
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If t is on the horizinal axis and f(t) is on the vertical axis (which is normal)

f(t) = 7/t;    t = a, t = a + h

f(a)=7/a

f(a+h)=7/(a+h)

The time difference between time=a and time=a+h is a+h-a=h (this is the horizonal difference)

f(a+h)-f(a) is the vertical difference

the average rate of change of the function is the

(difference between the function values at the end points)/(difference in time)

Like speed = distance/time OR

like the gradient of a line where A and B are two point on the line

=(difference between the y values  /difference in the x values )

Average rate of change= [f(a+h)-f(a)]/h

Jun 16, 2014
#2
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I am confused. Why aren't there any numbers or letters?

Jun 17, 2014
#3
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Because you were only given a's and h's .

would you like me to make up some numbers? (only joking)

would you like me to try and draw you a graph?

Jun 17, 2014
#4
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It keeps coming up as incorrect. That's why I am so confused. But I do understand how you got your answer...because there isn't anything else left.

Jun 17, 2014
#5
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This  is the introduction to calculus

See if this picture helps Jun 17, 2014
#6
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Jun 17, 2014
#7
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Its a mystery.............

Jun 17, 2014
#8
+10

I suspect sally1 is expecting this to be taken just a little further, so taking up where Melody left off:

(f(a+h) - f(a))/h = (7/(a+h) - 7/a)/h

= (7a - 7(a+h))/(a*(a+h)*h)

= -7h/(a*(a+h)*h)

= -7/(a*(a+h))

Alan Jun 17, 2014
#9
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Yes that is correct - Alan manipulated my answer to get the simplified answer that you wanted. 