If the length of the subnormal is equal to the length of the subtangent at the point…

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

If the length of the subnormal is equal to the length of the subtangent at the point

(3,4)

on the curve

y=f(x)

, and the tangent at

(3,4)

meets the coordinate axes at

A

and

B

, then the maximum area of

\triangle OAB

, where

O

is the origin, is (1)

\frac{45}{2}

(2)

\frac{49}{2}

(3)

\frac{25}{2}

(4)

\frac{81}{2}