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mathcalculus
Group Title
Determine the slope of the secant line for the curve defined by the equation:
(attached below)
 one year ago
 one year ago
mathcalculus Group Title
Determine the slope of the secant line for the curve defined by the equation: (attached below)
 one year ago
 one year ago

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genius12 Group TitleBest ResponseYou've already chosen the best response.1
The slope of the secant line is basically the average rate of change from \(\bf x_0\) to \(\bf x_1\). This is given by:\[\bf m_{secant}=A.R.C.H_{x_0}^{x_1}=\frac{ f(x_1)f(x_0) }{ x_1x_0 }\]
 one year ago

genius12 Group TitleBest ResponseYou've already chosen the best response.1
@mathcalculus Can you do that?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
is that like the differentiation but in other terms?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
@genius12
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
is it = to 1?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
do we substitute just for it?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
can we solve this together? @genius12
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
im stuck.
 one year ago

genius12 Group TitleBest ResponseYou've already chosen the best response.1
Ok I will solve step by step. Firstly, you should realise that this is essentially the slope formula which is:\[\bf m=\frac{ y_2y_1 }{ x_2x_1 }\]You remember that formula? @mathstudent55
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
that's the formula to find the slope .
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
are you there?
 one year ago

genius12 Group TitleBest ResponseYou've already chosen the best response.1
Well that what this essentially is! It's the slope, of the secant line, and the secant line is the line that connects the two points on the graph when x = 5 to when x = 6. I'll draw the graph and show to you:dw:1375078386992:dw
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
well i used that formula you gave me and i got 1/1
 one year ago

genius12 Group TitleBest ResponseYou've already chosen the best response.1
the y2 and y1 are such the y values at the 5 and 6. So plug in x = 5 and x = 6 in to f(x) = 2x^2  1 and find the yvalues of each. Now just calculate the slope with the:\[\bf m=\frac{y_2y_1}{x_2x_1}=\frac{ f(6)f(5) }{ 6(5) }\]
 one year ago

genius12 Group TitleBest ResponseYou've already chosen the best response.1
\[\bf f(6)=2(6)^21=73\]\[\bf f(5)=2(5)^21=51\]Plugging these values in we get:\[\bf slope_{secant}=\frac{ f(6)f(5) }{ 6(5) }=\frac{ 73(51) }{ 6(5) }=\frac{ 22 }{ 1 }=22\]
 one year ago

genius12 Group TitleBest ResponseYou've already chosen the best response.1
@mathcalculus That's what you are supposed to do. How did you get 1?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
so it;s 22?
 one year ago

genius12 Group TitleBest ResponseYou've already chosen the best response.1
Yes. How did you get 1?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
im not sure i did it the other way around.
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
hey, thank you so much , i'll be here tomorrow. need to sleep, thanks again. @genius12
 one year ago

genius12 Group TitleBest ResponseYou've already chosen the best response.1
Well I'll list out the steps for you. Find the yvalue at both xvalues. Here we were finding the slope of the secant line (the line that connects the two yvalues at x = 5 and x = 6). We first find the yvalue at x = 6 by plugging 6 for x in to f(x). Then we find yvalue at x = 5 by plugging in 5 for x. When we have these 2 yvalues, you just use the slope formula.
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
lol thank you ^_^
 one year ago
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