Let a curve , where for all , have the property that for every point on the curve,…

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

Let a curve

y=f(x)

, where

f(x)\geq0

for all

x\in\mathbb{R}

, have the property that for every point

P

on the curve, the length of the subnormal is equal to the abscissa of

P

. If

f(1)=3

, then

f(4)

is equal to (1)

-2\sqrt6

(2)

2\sqrt6

(3)

3\sqrt5

(4) None of these