If the tangent to the curve, y = x 3 + a x – b at the point ( 1 , – 5 ) is perpendicular to the line, – x + y + 4 = 0 , then which one of the following points lies on the curve?

Question

If the tangent to the curve, y = x 3 + a x &#8211; b at the point ( 1 , &#8211; 5 ) is perpendicular to the line, &#8211; x + y + 4 = 0 , then which one of the following points lies on the curve?

Quantrex Academy · Accepted Answer

Correct answer: A. 2 , &#160; &#8211; 2

Given y = x 3 + a x - b &#8757; it passes through 1 , - 5 &#8756; &#160; 1 + a - b = - 5 &#8658; a - b = - 6 &#160; &#160; &#160; . . . 1 Slope of the line a x + b y + c = 0 is - a b , hence, slope of the line - x + y + 4 = 0 is 1 We know that if two lines are perpendicular, then the product of their slopes is - 1 . &#8756; Slope of tangent of y , which is perpendicular to - x + y + 4 = 0 is - 1 Also, we know that the slop of tangent to a curve y = f x at a point x 1 , &#160; y 1 is given by f ' x 1 . &#8756; &

If the tangent to the curve, y = x 3 + a x – b at the point ( 1 , – 5 ) is perpendicular to the line, – x + y + 4 = 0 , then which one of the following points lies on the curve?

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Correct answer

Step-by-step solution

More from Application of Derivatives

If the tangent to the curve, y = x 3 + a x &#8211; b at the point ( 1 , &#8211; 5 ) is perpendicular to the line, &#8211; x + y + 4 = 0 , then which one of the following points lies on the curve?

Options

Correct answer

Step-by-step solution

More from Application of Derivatives

If the tangent to the curve, y = x 3 + a x – b at the point ( 1 , – 5 ) is perpendicular to the line, – x + y + 4 = 0 , then which one of the following points lies on the curve?