SOLUTION: Find the points on the graph y=7x/x-2 where the slope of the tangent line is parallel to the line 28x+2y-17=0

Question 1136952: Find the points on the graph y=7x/x-2 where the slope of the tangent line is parallel to the line 28x+2y-17=0
Found 2 solutions by rothauserc, greenestamps:
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
I assume you mean the following equation, always use parenthesis to clarify intent
:
y = 7x/(x-2)
:
use the quotient rule to find the first derivative
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let u be 7x and v be x-2
:
y' = 7 * ( (x-2)*1 - x(1) ) / (x-2)^2 = -14/(x-2)^2
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find slope of the given line by rewriting it as slope intercept form
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28x +2y -17 = 0
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2y = -28x +17
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y = -14x +17/2
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slope is -14, set first derivative equal to -14
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-14/(x-2)^2 = -14/1
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cross multiply fractions
:
-14(x-2)^2 = -14
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(x-2)^2 = 1
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x-2 = + or - 1
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x = 2 +1 = 3
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x = 2 -1 = 1
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we have two points whose x-coordinate is 3 or 1, we use the original equation to find the corresponding y coordinates
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f(3) = 7(3)/(3-2) = 21
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f(1) = 7(1)/(1-2) = -7
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the two points are (3,21) and (1,-7)
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:
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The purpose of this forum is to help you learn how to solve problems -- not to solve them for you.

This is a straightforward application of calculus; if you are working a problem like this, you should know what to do.

If you are having difficulty with a particular part of the problem, tell us what it is; that's what you are told to do when you post a problem. If you just post the problem without telling us what (if anything) you have tried, it looks as if you are just wanting us to work the whole problem for you.

The derivative of a function, evaluated at a particular value of x, gives you the slope of the tangent line to the function at that point (i.e., the "instantaneous slope"). The slope of the given line is found by putting the linear equation in slope-intercept form. The tangent line to the function and the given line are parallel when the slopes are the same.

So find the derivative of the given function and set it equal to the slope of the given line and solve for x. That gives you two x values where the slope of the tangent line to the function is equal to the slope of the given line; evaluate the function at each of those two points to finish the problem.
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