CAS MA 123 Lecture Notes - Lecture 37: Inflection, Minimal Surface

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Ma123 lecture 37 exam review: suppose f(x) is a positive decreasing function on [0, ) then what can you say about a(x) = x. 0 f (t ) dt : a(x) is an increasing function, a(x) is a decreasing function. Using ftc, f ( x ) dx - f ( x) dx = 5/12 - -8/3 = 37/12. 4 1: approximate the definite integral x. 1 dx using intervals and a midpoint reimann sum. Answer: 100 1/3: determine the intervals of concavity for f(x) = 5x4 20x3 +10 and identify any inflection points. Answer: concave up interval x>2 and x<0 and concave down (0,2)

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