Clavis TMUA Set C Paper 2 · Question 10

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Clavis TMUA Set C Paper 2 · Q10

Paper 2Calculus

The trapezium rule is used to estimate $\displaystyle\int_a^b f(x)\,dx$ , where $a<b$ .

Which one of the following conditions guarantees that the estimate is an overestimate?

f(x)>0

for all

x

with

a\leq x\leq b

f'(x)>0

for all

x

with

a\leq x\leq b

f''(x)>0

for all

x

with

a\leq x\leq b

f''(x)<0

for all

x

with

a\leq x\leq b

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