Question 1136952
I assume you mean the following equation, always use parenthesis to clarify intent
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y = 7x/(x-2)
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use the quotient rule to find the first derivative
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let u be 7x and v be x-2
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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
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-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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