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Determine the equation of the line AB

Line AB is a tangent to $2x^2 - 7x$

Line PD is perpendicular to AB

PD is represented by the equation $y = -x + 2$

To get the point of contact between the two lines, my math teacher said that it will be $f'(x) = 4x - 7 = -1$

Why is $f'(x) = 4x - 7 = -1$? Why will it not be $4x - 7 = 1$? Since: AB is a tangent and gradient is $1$ PD is perpendicular to AB and PD gradient is $-1$

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  • $\begingroup$ The question looks quite clear to me with a clear answer. Of two formulas for $x$ at the point of tangency, at most one can be correct; we are asked which is the correct one, and it is the student's formula. (Also, the OP clearly did all the work we could reasonably require before asking this!) $\endgroup$
    – David K
    Feb 15, 2016 at 21:04

2 Answers 2

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Slope of PD =-1. Slope of AB is +1 . Your last equation is quite correct. After finding x, find the y.

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Coefficient of x in the equation of line PD is $-1$. Negative reciprocal of that is $1$. So, your teacher is sadly wrong :/ since this tells us that $4x-7=1$

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