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anonymous
 4 years ago
Determine an equation of the line that is tangent to the graph of f(x) = sqrt (x+1) and parallel to x6y + 4= 0
anonymous
 4 years ago
Determine an equation of the line that is tangent to the graph of f(x) = sqrt (x+1) and parallel to x6y + 4= 0

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I found the derivative , which is the slope is 1/ 2 sqrt (x+1) what do i do next?

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1you need to find when that the derivative is the same as the slope of the given line what is the slope of the given line?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0get the derivative of sqrt (x1)...that's your equation of the tangent

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1what is the slope of x6y + 4= 0 ?

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1your derivative is wrong, by the way...

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0is it.... cuz if it is parallel, i can just plug in that slope to the equation..

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1maybe it's just your notation\[\frac d{dx}\sqrt{x+1}=\frac d{dx}(x+1)^{1/2}=\frac12(x+1)^{1/2}\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yea..it looks the same i have to solve it by limits

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1we need when that is the same as the slope of the given line. m:\[\frac12(x+1)^{1/2}=m\]oh you need the definition, eh? ok...

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1\[\frac{\sqrt{x+1+h}\sqrt{x+1}}h\]\[=\frac{\sqrt{x+1+h}\sqrt{x+1}}h\cdot\frac{\sqrt{x+1+h}+\sqrt{x+1}}{\sqrt{x+1+h}+\sqrt{x+1}}\]\[=\frac{x+1+hx1}{h\sqrt{x+1+h}+\sqrt{x+1}}=\frac{h}{h\sqrt{x+1+h}+\sqrt{x+1}}\]\[=\frac{1}{\sqrt{x+1+h}+\sqrt{x+1}}\]which in the limit is\[\frac1{2\sqrt{1+x}}\]so what have you got for m ?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0umm..isnt the answer of the derivative = the slope?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0and for the line, i got 1/6 as the slope..it looks wrong...i dont know

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1yes, and we want to know when that slope is the same as the slope of the given line\[\frac1{\sqrt{x+1}}=\frac16\]yes, 1/6 is what I got

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so do i find x using 1/2 sqrt (1+x) = 1/6 ?

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1yes, you need to know the point x for the pointslope form when we make our line

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0oh ok thanks!! i got x= 8 :)

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1so now you use the calculus version of pointslope form:\[yy_1=f'(x_1)(xx_1)\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0don't really get it ..

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0do u find a point and then plug in to y2 y1 /x 2 x1 = m?? i got 6y  x + 3 = 0 which is different from the textbook ans
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