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anonymous
 one year ago
Consider the function f(x) = 5 x  2 and find the following:
a) The average rate of change between the points (1, f(1) ) and (1, f( 1 ) ) .
b) The average rate of change between the points (a, f(a) ) and (b, f(b) ) .
c) The average rate of change between the points (x, f(x) ) and (x+h, f(x+h) ) .
anonymous
 one year ago
Consider the function f(x) = 5 x  2 and find the following: a) The average rate of change between the points (1, f(1) ) and (1, f( 1 ) ) . b) The average rate of change between the points (a, f(a) ) and (b, f(b) ) . c) The average rate of change between the points (x, f(x) ) and (x+h, f(x+h) ) .

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Average rate of change : \(A(x) = \dfrac{f(x)f(a)}{xa}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0where do i find a if like in a) i plug in 1 to the f(x) which is 5(1)2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[A(x) = \frac{f(1)  f(1)}{1 (1)}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Think you can handle the rest?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Just remember that the 2 points represent 2 coordinate points, and you're trying to find the slope \[A(x) = \frac{f(x)f(a)}{xa} \iff m = \frac{y_2 y_1}{x_2x_1}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0When you think about it this way, it's easier to identify which points subtract what, I guess

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohhh thats very helpful, thanks

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wait can you check my answers cause for a, i got 1 and for b i got a^2b^25. I think i plugged in wrong

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Think I might have stated the wrong values of x, but this is how i solved it. \[f(a)=f(1) = 3~,~f(x)= f(1) = 7\]\[m = \frac{f(x)f(a)}{xa} = \frac{7(3)}{1(1)} =\frac{10}{2}=5 \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh wow okay i was looking at a similar but different problem...I think i can do it now, thanks!

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.0Yeah it's basically \[\frac{ y_2y_1 }{ x_2x_1 }\] notice it's the slope formula @Jhannybean it's better to write the equation as \[m = \frac{ f(b)f(a) }{ ba }\] to avoid confusion

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0And i figured I switched it because when you solve the last one with \((x~,~ f(x))\) and \((x+h,~f(x+h))\) you will get the definition of a derivative once you take the limit of it, but that's for later i guess. Therefore I knew i made a mistake.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so you have (x, f(x) ) and (x+h, f(x+h) ) Which translates into \[m= \frac{f(x+h)f(x)}{(x+h)x}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh i just leave the f(x)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Hm? Nothing changes in the numerator, it's only the denominator that you're concerned wtih.
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