If the normal to the curve $y = x ln x$ $y=xlnx$ is parrallel to the straight line $2 x - 2 y + 3 = 0$ $2x-2y+3=0$ ,then the normal equation is...... a. $x - y = 3 e^{- 2}$ $x-y=3e^-2$ b. $x - y = 6 e^{- 2}$ $x-y=6e^-2$ c. $x - y = 3 e^{2}$ $x-y=3e^2$ ?

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If the normal to the curve $y = x ln x$ $y=xlnx$ is parrallel to the straight line $2 x - 2 y + 3 = 0$ $2x-2y+3=0$ ,then the normal equation is...... a. $x - y = 3 e^{- 2}$ $x-y=3e^-2$ b. $x - y = 6 e^{- 2}$ $x-y=6e^-2$ c. $x - y = 3 e^{2}$ $x-y=3e^2$ ?

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Answer 1 · 2018-05-10T19:43:08

Option A is correct .

Explanation:

The line can be rewritten a

$2 x + 3 = 2 y$ $2x + 3 = 2y$

$x + \frac{3}{2} = y$ $x + 3/2 = y$

So the slope of the line (as well as the normal line) will be $1$ $1$ . This means the slope of the tangent will be $- 1$ $-1$ , so we have to set the derivative to $- 1$ $-1$ .

$y' = lnx + x(1/x) = lnx + 1$

We have:

$-1= lnx + 1 -> lnx = -2 -> x = e^-2$

The corresponding value of $y$ is $y = e^-2ln(e^-2) = -2e^-2$

We now can see that the normal has equation

$y - (-2e^-2) = x - e^-2$

$y = x - e^-2 - 2e^-2$

$y = x - 3e^-2$

Or

$x - y = 3e^-2$

Which is option A.

Hopefully this helps!

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If the normal to the curve $y = x ln x$ $y=xlnx$ is parrallel to the straight line $2 x - 2 y + 3 = 0$ $2x-2y+3=0$ ,then the normal equation is...... a. $x - y = 3 e^{- 2}$ $x-y=3e^-2$ b. $x - y = 6 e^{- 2}$ $x-y=6e^-2$ c. $x - y = 3 e^{2}$ $x-y=3e^2$ ?

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Explanation:

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If the normal to the curve y=xlnxy=xlnxy=xlnx is parrallel to the straight line 2x-2y+3=02x−2y+3=02x-2y+3=0 ,then the normal equation is...... a.x-y=3e^-2x−y=3e−2x-y=3e^-2 b.x-y=6e^-2x−y=6e−2x-y=6e^-2 c.x-y=3e^2x−y=3e2x-y=3e^2 ?

1 Answer

Explanation:

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If the normal to the curve $y = x ln x$ $y=xlnx$ is parrallel to the straight line $2 x - 2 y + 3 = 0$ $2x-2y+3=0$ ,then the normal equation is...... a. $x - y = 3 e^{- 2}$ $x-y=3e^-2$ b. $x - y = 6 e^{- 2}$ $x-y=6e^-2$ c. $x - y = 3 e^{2}$ $x-y=3e^2$ ?