Let f : I R be differentiable at c I. Establish the Straddle Lemma: Given > 0 there exists (e) > 0

Let f : I → R be differentiable at c ∈ I. Establish the Straddle Lemma: Given ε > 0 there exists δ(e) > 0 such that if u, v ∈ I satisfy c - δ(e) < u < c < v < c + δ(e), then we have f(v) - f(u) - (v - u) fʹ(c)| < e(v - u). [The δ(e) is given by Definition 6.1.1. Subtract and add the term f(c) - cfʹ(c) on the left side and use the Triangle Inequality.]