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anonymous
 2 years ago
Determine the slope of the secant line for the curve defined by the equation:
(attached below)
anonymous
 2 years ago
Determine the slope of the secant line for the curve defined by the equation: (attached below)

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anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0The slope of the secant line is basically the average rate of change from \(\bf x_0\) to \(\bf x_1\). This is given by:\[\bf m_{secant}=A.R.C.H_{x_0}^{x_1}=\frac{ f(x_1)f(x_0) }{ x_1x_0 }\]

anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0@mathcalculus Can you do that?

anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0is that like the differentiation but in other terms?

anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0do we substitute just for it?

anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0can we solve this together? @genius12

anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0Ok 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

anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0that's the formula to find the slope .

anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0Well 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

anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0well i used that formula you gave me and i got 1/1

anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0the 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:\[\bf m=\frac{y_2y_1}{x_2x_1}=\frac{ f(6)f(5) }{ 6(5) }\]

anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0\[\bf f(6)=2(6)^21=73\]\[\bf f(5)=2(5)^21=51\]Plugging these values in we get:\[\bf slope_{secant}=\frac{ f(6)f(5) }{ 6(5) }=\frac{ 73(51) }{ 6(5) }=\frac{ 22 }{ 1 }=22\]

anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0@mathcalculus That's what you are supposed to do. How did you get 1?

anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0Yes. How did you get 1?

anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0im not sure i did it the other way around.

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

anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0Well 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.
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