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Question

Let C be a curve given by y(x)=1+4x3,x>34. If P is a point on C, such that the tangent at P has slope 23, then a point through which the normal at P passes, is:

A
(3,4)
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B
(1,7)
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C
(2,3)
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D
(4,3)
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Solution

The correct option is B (1,7)
y=1+4x3dydx=124x3×4=23x=3,y=1+3=4Slope of the normal=32Equation of the normal is,y4=32(x3)3x+2y17=0Which passes through (1,7)

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