Science:Math Exam Resources/Courses/MATH110/December 2017/Question 09/Statement

Use the Intermediate Value Theorem to show that there is a number ${\textstyle x=c}$ in the interval ${\textstyle (0,2)}$ such that the tangent line to the graph of ${\textstyle f(x)={\frac {1}{4}}x^{4}+x}$ at ${\textstyle x=c}$ is parallel to the tangent line to the graph of ${\textstyle g(x)={\frac {1}{6}}x^{6}}$ at ${\textstyle x=c}$. Is ${\textstyle c}$ closer to 0 or 2?