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Determine the slope of the secant line for the curve defined by the equation:
(attached below)
 8 months ago
 8 months ago
Determine the slope of the secant line for the curve defined by the equation: (attached below)
 8 months ago
 8 months ago

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genius12Best 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:\[\bf m_{secant}=A.R.C.H_{x_0}^{x_1}=\frac{ f(x_1)f(x_0) }{ x_1x_0 }\]
 8 months ago

genius12Best ResponseYou've already chosen the best response.1
@mathcalculus Can you do that?
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
is that like the differentiation but in other terms?
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
do we substitute just for it?
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
can we solve this together? @genius12
 8 months ago

genius12Best 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
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
that's the formula to find the slope .
 8 months ago

genius12Best 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
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
well i used that formula you gave me and i got 1/1
 8 months ago

genius12Best 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:\[\bf m=\frac{y_2y_1}{x_2x_1}=\frac{ f(6)f(5) }{ 6(5) }\]
 8 months ago

genius12Best 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:\[\bf slope_{secant}=\frac{ f(6)f(5) }{ 6(5) }=\frac{ 73(51) }{ 6(5) }=\frac{ 22 }{ 1 }=22\]
 8 months ago

genius12Best ResponseYou've already chosen the best response.1
@mathcalculus That's what you are supposed to do. How did you get 1?
 8 months ago

genius12Best ResponseYou've already chosen the best response.1
Yes. How did you get 1?
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
im not sure i did it the other way around.
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
hey, thank you so much , i'll be here tomorrow. need to sleep, thanks again. @genius12
 8 months ago

genius12Best 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.
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
lol thank you ^_^
 8 months ago
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