# Science:Math Exam Resources/Courses/MATH100/December 2018/Question 11 (b)

MATH100 December 2018
Other MATH100 Exams

### Question 11 (b)

Let ${\displaystyle g(x)}$ be a twice differentialble function with a continuous second derivative and also, satisfying the property that

${\displaystyle {\frac {x}{2}}\leq g(x)\leq {\frac {x}{2}}+1}$

for each positive real number ${\displaystyle x}$. We let ${\displaystyle f(x)=g(x)+\sin(x)}$.

Prove that there exist infinitely many real numbers ${\displaystyle c}$ such that ${\displaystyle f''(c)=0}$.

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