**Unformatted text preview: **) . Suppose that f is diﬀerentiable on ( a,c ) and ( c,b ) . (a) Prove the following test for determining whether c is a relative minimum: If there is a neighborhood ( c-δ,c + δ ) ⊆ [ a,b ] such that ● for all x ∈ ( c-δ,c ) , f ′ ( x ) ≤ 0, ● and, for all x ∈ ( c,c + δ ) , f ′ ( x ) ≥ 0, then f has a relative minimum at c . (b) Write down the analogue for a relative maximum....

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- Spring '08
- JUNGE
- Math, Calculus, Mean Value Theorem, Mathematical analysis, relative minimum, elementary real analysis