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Asked Oct 2, 2019
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59. Find equations of both lines that are tangent to the curve
3x23x-3 and are parallel to the line
y =x3
Зх — у 3D 15.
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59. Find equations of both lines that are tangent to the curve 3x23x-3 and are parallel to the line y =x3 Зх — у 3D 15.

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Expert Answer

Step 1

First we find the slope of the tangent:

Slope of the tangent is the derivative of the given curve.

Therefore differentiating given function with respect to x, we get

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d slope of the tangent = = 3x -3(2.x)+3(1)-0 dc =n . = 3x2 -6x3

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Step 2

Now we find the slope of the given line:

 

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Given line is 3x -y = 15 y 3x -15 Comparing with y = mx +c , we get slope m 3

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Step 3

Since tangents are parallel to the given line, therefore their slopes must ...

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3x2 - 6x 3 3 x2-2x +1 1 >x'-2x x(x-2)0 x 0 or x-2 =0 x 0 or x =2

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Tagged in

Math

Calculus

Derivative