tmua 2018 Q18

tmua · Uk · paper2 1 marks Completing the square and sketching Sign analysis of quadratic coefficients and expressions from a graph

$\mathrm { f } ( x )$ is a polynomial function defined for all real $x$.
Which of the following is a necessary condition for the inequality
$$\frac { \mathrm { f } ( a ) + \mathrm { f } ( b ) } { 2 } \geq \mathrm { f } \left( \frac { a + b } { 2 } \right)$$
to be true for all real numbers $a$ and $b$ with $a < b$ ?

..... 20

$\mathrm { f } ( x )$ is a polynomial function defined for all real $x$.

Which of the following is a necessary condition for the inequality

$$\frac { \mathrm { f } ( a ) + \mathrm { f } ( b ) } { 2 } \geq \mathrm { f } \left( \frac { a + b } { 2 } \right)$$

to be true for all real numbers $a$ and $b$ with $a < b$ ?

Paper Questions

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