Question

# 1. Let y = f(x) be any curve and P be any point on it then the slope of the curve at P is dydx=m=tanθ 2. Equation of the tangent at P is y−y1=m(x−x1) 3. Equation of the normal at P is y−y1=−1m(x−x1) On the basis of these 3 points answer the following questions: At what points on the curve y=23x3+12x2, tangent makes equal angle with axes

A
(12,524) and (1,16)
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B
(12,49) and (1,0)
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C
(13,17) and (3,12)
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D
(13,427) and (1,13)
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Solution

## The correct option is A (12,524) and (−1,−16)dydx=±1 ∴2x2+x−1=0 x=−1,12 ∴ The points are (−1,−16),(12,524) y=ax2+6x+b...(1) In equation (1) by putting x = 0, y = 2 We get ⇒b=2 Equation (2) ∣∣dydx∣∣at x=32=0⇒3a+6=0⇒a=−2.

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