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avatar+253 

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
sally1  Jun 16, 2014

Best Answer 

 #8
avatar+26329 
+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
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10+0 Answers

 #1
avatar+91051 
+10

 

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

Melody  Jun 16, 2014
 #2
avatar+253 
+5

I am confused. Why aren't there any numbers or letters?

sally1  Jun 17, 2014
 #3
avatar+91051 
+10

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?

Melody  Jun 17, 2014
 #4
avatar+253 
+5

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.

sally1  Jun 17, 2014
 #5
avatar+91051 
+5

This  is the introduction to calculus

See if this picture helps

Melody  Jun 17, 2014
 #6
avatar+91051 
0

what does your answer come up as?

Melody  Jun 17, 2014
 #7
avatar+4155 
0

Its a mystery.............

zegroes  Jun 17, 2014
 #8
avatar+26329 
+10
Best Answer

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
avatar+253 
0

Alan's answer was correct. So I suppose I put both your answer and his answer together?

sally1  Jun 17, 2014
 #10
avatar+91051 
+5

Yes that is correct - Alan manipulated my answer to get the simplified answer that you wanted. 

Melody  Jun 18, 2014

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