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  • Find the points on the curve at which the tangent lines are parallel to the line <img alt="4x + y - 3= 0" src=

Find the points on the curve y = x^{3} -3x^{2} - 4x at which the tangent lines are parallel to the line 4x + y - 3= 0

 

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Slope of line 4x + y - 3= 0 is -4.

\\y = x^{3} -3x^{2} - 4x \\\\ \frac{dy}{dx} = 3x^2 -6x - 4

\\ \frac{d y}{d x}=-4 \\\\ 3 x^{2}-6 x-4=-4 \\\\ 3 x(x-2)=0 \\ x=0 , x=2 \\

Hence the Point  the curve are (0,0) , (2,-12) where the tangent is parallel to given line.

Posted by

Safeer PP

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