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Question

If the normal to the curve y=f(x) at the point (3,4) makes 3π4 with the positive x-axis then f'(3) =?


A

-1

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B

-34

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C

43

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D

1

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Solution

The correct option is D

1


Explanation for the correct answer:

The normal makes an angle of 3π4 with the positive x-axis.

Let the slope of the normal be mn

mn=tan3π4

=tanπ-π4

=-tanπ4

mn=-1...(i)

The first order derivative of the equation of the curve at a point gives the slope of the tangent to the curve at that point.

Let mt be the slope of the tangent to the curve at point (3,4)

dydx3,4=f'x=mt

mt=f'(3)...(ii)

The tangent and the normal are perpendicular to each other. Hence, the product of their slopes is -1.

mt×mn=-1

From (i),(ii) we get

f'3×-1=-1

f'3=1

So, option (D) is the correct answer.


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