+9481 (a) Here's a graph: https://www.desmos.com/calculator/fxto5gtfns
(b) P = (2, 8) Q = (x, x3)
Find the slope of the line PQ for the following values of x .
When x = 1.5, Q = (1.5, 1.53) = (1.5, 3.375)
We want to find the slope of the line passing through the points (2, 8) and (1.5, 3.375)
slope = \(\frac{8-f(1.5)}{2-1.5}\,=\,\frac{8-3.375}{2-1.5}\,=\,\frac{4.625}{0.5}\,=\,9.25\)
This is the first value for the slope of the secant on the table.
| x | msec | |
| 1.5 | 9.25 | |
| 1.9 | \(\frac{8-f(1.9)}{2-1.9}\,=\,\frac{8-6.859}{2-1.9}\,=\,\frac{1.141}{0.1}\,=\,11.41\) | |
| 1.99 | \(\frac{8-f(1.99)}{2-1.99}\,=\,\frac{8-7.880599}{2-1.99}\,=\,\frac{0.119401}{0.01}\,=\,11.9401\) | |
| 2 | ? | |
| 2.01 | \(\frac{8-f(2.01)}{2-2.01}\,=\,\frac{8-8.120601}{2-2.01}\,=\,\frac{-0.120601}{-0.01}\,=\,12.0601\) | |
| 2.1 | \(\frac{8-f(2.1)}{2-2.1}\,=\,\frac{8-9.261}{2-2.1}\,=\,\) |
Do you see how I am doing these? See if you can finish the table...
(c)
The slope of the tangent line when x = 2 appears to be between 11.9401 and 12.0601
Let's just take the average of these two... (11.9401 + 12.0601) / 2 = 12.0001
So I'd guess that the slope of the tangent line at (2, 8) is 12 
+118689 Hi HelperId
Look back here. These are on the original thread.
https://web2.0calc.com/questions/very-hard-math-question-for-my-profile-picture#r8
and a better response here:
https://web2.0calc.com/questions/very-hard-math-question-for-my-profile-picture#r9
I have not answered I have just worked out why you keep re-asking and why you were not happy with Heureka's ealier answer.
I have not looked at the guests answer on your last re-ask. So I cannot say whether or not it was relevant or helpful.
+118689 Helper Id you hae reposted thit same question in all these future spots
https://web2.0calc.com/questions/very-hard-math-question-for-my-profile-picture-repeat
https://web2.0calc.com/questions/very-hard-math-question-for-my-profile-picture-rerepost
https://web2.0calc.com/questions/very-hard-question-for-my-profile-picture
Thanks for reposting in the correct way. Each time you have bought us back to your original question very nicely and I appreciate that.
I do not understand however why you are still asking this.
You did give an explanation here:
https://web2.0calc.com/questions/very-hard-math-question-for-my-profile-picture-repeat#r1
Heureka did originally put the hyperbola through the wrong points, that is true, but when I pointed out his error he redid it through what lookes to be the correct points. You have not told us what the points are so we did have to estimate them from the pic.
This is where heureka re-answered.
https://web2.0calc.com/questions/very-hard-math-question-for-my-profile-picture#r6
I do not understand why you are not accepting this answer. What is wrong with it?
It goes through the points (2.75,2.75) (1.75,5) and (5,1.75)
Why are you not happy with this #6 answer ?????
