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anonymous
 one year ago
The point P(9 , 6 ) lies on the curve y = \sqrt{ x } + 3. Let Q be the point (x, \sqrt{ x }+ 3 ).
a.) Find the slope of the secant line PQ for the following values of x(Answers here should be correct to at least 6 places after the decimal point.)
If x= 9.1, the slope of PQ is:
If x= 9.01, the slope of PQ is:
If x= 8.9, the slope of PQ is:
If x= 8.99, the slope of PQ is:
b.) Based on the above results, estimate the slope of the tangent line to the curve at P(9 , 6 ).
anonymous
 one year ago
The point P(9 , 6 ) lies on the curve y = \sqrt{ x } + 3. Let Q be the point (x, \sqrt{ x }+ 3 ). a.) Find the slope of the secant line PQ for the following values of x(Answers here should be correct to at least 6 places after the decimal point.) If x= 9.1, the slope of PQ is: If x= 9.01, the slope of PQ is: If x= 8.9, the slope of PQ is: If x= 8.99, the slope of PQ is: b.) Based on the above results, estimate the slope of the tangent line to the curve at P(9 , 6 ).

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jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1If x= 9.1, then what is the value of y?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Of the original function or the derivative?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1original function

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0y = \sqrt{ x } + 3 at x=9.1 > 6.016620626

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1so we know the point (9.1, 6.016620626) lies on the function curve

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1P = (9,6) Q = (9.1, 6.016620626) slope of PQ = ??

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0that's what I don't get, I do not know what to do...

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1you would use the slope formula \[\LARGE m = \frac{y_{2}y_{1}}{x_{2}x_{1}}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it doesn't work because both x are 9 (we cannot divide by 0)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1x1 = 9 x2 = 9.1

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1so x2  x1 = 9.1  9 = 0.1

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh i missed that one, the answer is 0.16620626 ... would that be the answer for the first one?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I entered it and it says correct!! thank you! what about b) ?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1y1 = 6 y2 = 6.016620626 y2  y1 = 6.016620626  6 = 0.016620626 divide that by 0.1 and you get 0.016620626/0.1 = 0.16620626 so it looks good

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1repeat the same steps as a) but now use x = 9.01 instead of 9.1

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I meant the second part of the question

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1tell me what slopes you get for part a)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0for every one of them of just the first one?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.00.16620626 0.16662039610.16713221960.1667129887

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0We just do the average?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1it's probably not 100% clear but what do you notice that is common to all of these slopes?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I tried the average of them and it is correct! Thank you so much, I appreciate it greatly! Could you help me with another quick question?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Let f(x) = 3x^{4}4. (a) Use the limit process to find the slope of the line tangent to the graph of f at x = 3. Slope at x = 3: (I got 324 but i dont know if it is correct) (b) Find an equation of the line tangent to the graph of f at x = 3. Tangent line: y =

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Do you know how to help me on this one?

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0dw:1443842056603:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1keep following @triciaal steps to find the value of f(3) if x = 3, then y = ??

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1so we know (3,239) lies on the curve

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and the slope of 324 was correct?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1so you know this line has a slope of 324 and goes through (3,239)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1m = 324 (x1,y1) = (3,239)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0How do you rearrange it so that the equation looks like y= mx+b ??

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1you just need to solve for y and simplify

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It worked! I just made a sign mistake at the end.... @jim_thompson5910 I appreciate your help greatly! you saved my grade! @triciaal Thank you also for helping me I appreciate it

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1you're welcome
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