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

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

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

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

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

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

genius12
 one year ago
Best ResponseYou've already chosen the best response.1Ok 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

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

genius12
 one year ago
Best ResponseYou've already chosen the best response.1Well 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

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

genius12
 one year ago
Best ResponseYou've already chosen the best response.1the 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:\[\bf m=\frac{y_2y_1}{x_2x_1}=\frac{ f(6)f(5) }{ 6(5) }\]

genius12
 one year ago
Best 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:\[\bf slope_{secant}=\frac{ f(6)f(5) }{ 6(5) }=\frac{ 73(51) }{ 6(5) }=\frac{ 22 }{ 1 }=22\]

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

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

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

mathcalculus
 one year 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

genius12
 one year ago
Best ResponseYou've already chosen the best response.1Well 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.

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