tmua 2019 Q14

tmua · Uk · paper2 1 marks Stationary points and optimisation

Consider the following statements about the polynomial $\mathrm { p } ( x )$, where $a < b$ :
I $\quad \mathrm { p } ( a ) \leq \mathrm { p } ( b )$
II $\quad \mathrm { p } ^ { \prime } ( a ) \leq \mathrm { p } ^ { \prime } ( b )$
III $\mathrm { p } ^ { \prime \prime } ( a ) \leq \mathrm { p } ^ { \prime \prime } ( b )$
Which of these statements is a necessary condition for $\mathrm { p } ( x )$ to be increasing for $a \leq x \leq b$ ?

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Consider the following statements about the polynomial $\mathrm { p } ( x )$, where $a < b$ :

I $\quad \mathrm { p } ( a ) \leq \mathrm { p } ( b )$

II $\quad \mathrm { p } ^ { \prime } ( a ) \leq \mathrm { p } ^ { \prime } ( b )$

III $\mathrm { p } ^ { \prime \prime } ( a ) \leq \mathrm { p } ^ { \prime \prime } ( b )$

Which of these statements is a necessary condition for $\mathrm { p } ( x )$ to be increasing for $a \leq x \leq b$ ?

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20