TMUA DPiD Maths Mock Set 1 Paper 2 · Question 10

Let $f(x)$ and $g(x)$ be functions whose derivatives $f'(x)$ and $g'(x)$ exist for all real numbers. Which of the following statements is implied by exactly five of the others?

f(x)=g(x)

for all

x

in the interval

[0,2]

f

and

g

are polynomials with

f(k)=g(k)

for each of

k=0,1,2,3

f(x)=g(x+2)=f(x+4)

for all real numbers

x

f'(r)=g'(r)

for some real number

r

f(x)>g(x)

for all real numbers

x

f(x)=g(x)

for all real numbers

x

f

and

g

are both constant functions.

HNone of the statements implies any other.

examday

DPiD Maths Mock Set 1 Paper 2 · Q10