TMUA Official 2020 Paper 2 · Question 12

Which one of A–F correctly completes the following statement?

Given that $a<b$ , and $f(x)>0$ for all $x$ with $a<x<b$ , the trapezium rule produces an overestimate for $\displaystyle\int_a^b f(x)\,\dd x$ …

A… if

f'(x)>0

and

f''(x)<0

for all

x

with

a<x<b

B… only if

f'(x)>0

and

f''(x)<0

for all

x

with

a<x<b

C… if and only if

f'(x)>0

and

f''(x)<0

for all

x

with

a<x<b

D… if

f'(x)<0

and

f''(x)>0

for all

x

with

a<x<b

E… only if

f'(x)<0

and

f''(x)>0

for all

x

with

a<x<b

F… if and only if

f'(x)<0

and

f''(x)>0

for all

x

with

a<x<b

examday