2x = See CalcChat.com for tutorial help and worked-out solutions to odd-numbered exercises. 47. fx) 48.Hx) = x Think Abou function f Intervals on Which a Function Is Increasing or In Exercises 1-8, n the closed interval. Decreasing In Exercises 21-26, find the open which the function is increasing or decreasing intervals 49. f(0) =f( f(3) = f' f (x) > Of f (x) >0f f (x) < Of f"(x) < 0 on =+6x, [-6, 1] -3 [0,9] 22. h(x) = (x + 2)1/3 +8 21. f(x) = x2 +3x- 12 23. f(x) = (x -1)2(2x 5) 24. g(x) = (x + 1)3 25. h(x) = Vx(x - 3), x > 0 x [0, 2] 0 x< 2T 26. f(x) = sinx + cos x, 1 Applying the First Derivative Test In Exercises 27-34, (a) find the critical numbers of f, if any, (b) find the open intervals on which the function is increasing or (c) apply the First Derivative Test to identify all relative extrema, and (d) use a graphing utility to confirm your results f"(x)> Of s9-12, determine to f on the closed decreasing, 51. Writin grow e applied, find all h that f'(c) = 0. If why not. 28. f(x) 4x3- 5x me 27. f(x) = x2- 6x+ 5 3-8x 30. f(x) 29. f(t) = 4 8t 4 x2 - 3x-4 32. f(x) = 31. f(x) = x-2 33. f(x) = , ) cos x-sin x, 3 TX sin 2 , 4) 34. f(x) Exercises 13-18, can be applied to alue Theorem can 2 Motion Along a Line In Exercises 35 and 36, the f s(t) describes the motion of a particle along a line. (a) Fin velocity function of the particle at any time t 0. (b) Identh, the time interval (s) on which the particle is moving in a direction. (c) Identify the time interval(s) on which the par Is moving in a negative direction. (d) Identify the times) a which the particle changes direction. val (a, b) such that 5C positive , explain why not. 35. s(t) 3t - 212 36. S(t) = 613 -8t+ 3 Finding Points of Inflection In Exercises 37-42, find the points of inflection and discuss the concavity of the graph of the function. 37. f(x) = x3 - 9x2 (a) Use the re 38. f(x) = 6x4 -x 39. g(x) = x /x +5 a model of D = at Value Theorem be 40. f(x) = 3x - 5x ar4 41. f(x) = x + cos x, 0, 2T for the S
Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.
Arcs in Circles
A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.
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