TMUA Euclid Sample Paper 1 · Question 16

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Euclid Sample Paper 1 · Q16

Paper 1GeometryFunctions & graphs

A differentiable function $f:(0,\infty)\to\mathbb R$ satisfies

f'(x)=-\frac4{x^2}.

For each $t>0$ , the tangent to the curve $y=f(x)$ at $x=t$ meets the coordinate axes at $P_t$ and $Q_t$ . Let $A_t$ be the area of triangle $OP_tQ_t$ , where $O$ is the origin. It is given that

A_2=A_5.

What is the value of $A_7$ ?

0

\frac89

2

4

6

8

16

HIt cannot be determined

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