1. The problem statement, all variables and given/known data Let [tex]h[/tex] be a differentiable function defined on the interval [tex][0,3][/tex], and assume that [tex]h(0) = 1, h(1) = 2[/tex] and [tex]h(3) = 2[/tex]. (c) Argue that [tex]h'(x) = 1/4[/tex] at some point in the domain. 2. Relevant equations (a) Argue that there exists a point [tex]d \in [0,3][/tex] where [tex]h(d) = d[/tex]. (b) Argue that at some point [tex]c[/tex], we have [tex]h'(c) = 1/3[/tex] 3. The attempt at a solution This question comes in 3 parts and I've already solved parts (a) and (b). Part (a) is simply by the intermediate value theorem, using the fact that differentiation implies continuity and that continuous functions have the intermediate value property. Part (b) is by the mean value theorem. So those two parts I'm fine, but I'm kind of stuck on part (c). I'm convinced that part (c) has something to do with the mean value theorem. And tips would be appreciated here! Thanks!