Unattributed TMUA Mock Set A Paper 1 · Question 14

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Unattributed TMUA Mock Set A Paper 1 · Q14

Paper 1CalculusFunctions & graphsPowers & logarithms

The derivative of the function $f(x)$ is $f'(x)$ . If there exists $x_0$ such that $f(x_0)=f'(x_0)$ , then $x_0$ is a coincidence point of $f(x)$ . How many of the following functions have a coincidence point?

I. $x$
II. $x^2$
III. $\dfrac1x$
IV. $\ln x$
V. $\left(\dfrac1e\right)^x$

0

1

2

3

4

5

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