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

1. mathcalculus

2. genius12

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:$\bf m_{secant}=A.R.C.H|_{x_0}^{x_1}=\frac{ f(x_1)-f(x_0) }{ x_1-x_0 }$

3. genius12

@mathcalculus Can you do that?

4. mathcalculus

is that like the differentiation but in other terms?

5. mathcalculus

@genius12

6. mathcalculus

is it = to 1?

7. mathcalculus

do we substitute just for it?

8. mathcalculus

can we solve this together? @genius12

9. mathcalculus

im stuck.

10. genius12

Ok I will solve step by step. Firstly, you should realise that this is essentially the slope formula which is:$\bf m=\frac{ y_2-y_1 }{ x_2-x_1 }$You remember that formula? @mathstudent55

11. mathcalculus

yes

12. mathcalculus

that's the formula to find the slope .

13. mathcalculus

are you there?

14. genius12

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|

15. mathcalculus

well i used that formula you gave me and i got 1/1

16. genius12

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 y-values of each. Now just calculate the slope with the:$\bf m=\frac{y_2-y_1}{x_2-x_1}=\frac{ f(-6)-f(-5) }{ -6-(-5) }$

17. genius12

$\bf f(-6)=-2(-6)^2-1=-73$$\bf f(-5)=-2(-5)^2-1=-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$

18. genius12

@mathcalculus That's what you are supposed to do. How did you get 1?

19. mathcalculus

so it;s 22?

20. genius12

Yes. How did you get 1?

21. mathcalculus

im not sure i did it the other way around.

22. mathcalculus

hey, thank you so much , i'll be here tomorrow. need to sleep, thanks again. @genius12

23. genius12

Well I'll list out the steps for you. Find the y-value at both x-values. Here we were finding the slope of the secant line (the line that connects the two y-values at x = -5 and x = -6). We first find the y-value at x = -6 by plugging -6 for x in to f(x). Then we find y-value at x = -5 by plugging in -5 for x. When we have these 2 y-values, you just use the slope formula.

24. mathcalculus

lol thank you ^_^