Calculus

Chapter 4. Applications of 1st and 2nd Derivatives (Sketching of Curves) 4.2 Increasing & Decreasing Functions rendering 4.2 .1 A make f is said to i) increase on the interval I if for every 2 rime [pic] in I, [pic]implies that [pic] ii) fall(a) on the interval I if for every 2 numbers [pic] in I, [pic]implies that [pic] Theorem 4.2.2 Suppose that f is differentiable on an adequate to(p) interval I i) If[pic] for all x in I, then f increases on I ii) If[pic] for all x in I, then f decreases on I iii) If[pic] for all x in I, then f is constant on I (refer to figures 4.2.1-4.2.6) [pic] 4.3 topical anesthetic Extreme Values Definition 4.3 .1 Local Extreme Values Suppose that f is a function and c is an interior point of the domain. The function f is said to imbibe a local or relative maximum at c provided that [pic] for all x sufficiently close to c. The function f is said to have a local or relative minimum at c provided that [pic] for all x sufficiently close to c. The local or relative maxima and minima of f comprise the local extreme values of f (refer to figure 4.3.1) Definition 4.3 .

3 Critical Points The interior points c of the domain of f for which [pic]or [pic] does non exist or f is not differentiable are called the critical points of f. ( refer to figures 4.3.2-4.3.3) [pic] Theorem 4.3.4 The 1st Derivative Test Suppose that c is a critical point for f and f is never-ending at c. If there is a positive number [pic]such that: i) If[pic] for all x in [pic] and [pic]for all x in[pic], then [pic]is a local or relative maximum ii) If[pic] for all x in [pic] and [pic]for all x in[pic], then [pic]is a local or relative minimum iii) If[pic] keeps constant sign on [pic] [pic][pic], then [pic]is not a... If you want to get a full essay, order it on our website: Orderessay

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