Let be a twice differentiable function in such that and

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Let f:[0,1]→Rf:[0,1] \rightarrow R be a twice differentiable function in (0,1)(0,1) such that f(0)=3f(0)=3 and f(1)=5f(1)=5. If the line y=2x+3y=2x+3 intersects the graph of ff at only two distinct points in (0,1)(0,1), then the least number of points x∈(0,1)x \in (0,1), at which f′′(x)=0f''(x)=0, is

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