Does The Parabola Y = 2x^2 - 13x + 5 Have A Tangent Whose Slope Is -1. If So, Then It Will Be? - Testpoint

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Does the parabola y = 2x^2 - 13x + 5 have a tangent whose slope is -1. If so, then it will be?

y= -x-13
y= 2x+2
y= x^2-1
None of these

Explanation

Given:

$y = 2 x^^{2} - 13 x + 5$

Differentiate:

$d y/$ dx=4x−13

For slope $= - 1$ :

$4 x - 13 = - 1$ $x = 3$

At $x = 3$ :

$y = 2 (3)^^{2} - 13 (3) + 5 = - 16$

So the point of contact is (3, −16).

The tangent equation:

$y + 16 = - (x - 3)$

y=−x−13

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