%%visits: 2 Finding the global extrema - find all c1, c2, … ∈ [a, b] where f′(ck) = 0 (also second derivate if there are too many minima) - evaluate f(ck)∀k - evaluate f(a), f(b) - select the maximal value from the list f(a), f(b), f(c1), f(c2)
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Let f be defined on ℝ. If f(x) = ax + b + o(1) as x → ∞, we say that the line y = ax + b is an asymptote of the graph of f.
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To sketch the graph of f(x), follow these steps: - Find the natural domain of f - Investigate the limiting behaviour at the boundary of the natural domain. If this includes infinity, determine the asymptotes at infinity - Find intervals of continuity, find discontinuity and types - Find zeros and intervals of constant sign - Find extrema and intervals of monotonicity - Find the intervals of convexity