f(x) =8<:x|x|ifx <00ifx= 0x-cosxifx >0If you thinkfis not continuous atx= 0, what kind of discontinuity isit?5. (10 points) Calculate the equation of the tangent line to the curvedefined byx3+y3= 2xyat the point, (1,1).6. Letf(x) = 4 + 8x3-x4(a) (2 points) Over whatx-intervals isfincreasing/decreasing?(b) (2 points) Find all critical points offand test each for localmaximum and local minimum.(c) (3 points) Over whatx-intervals isfconcave up/down?(d) (3 points) Sketch the shape of the graph off.7. Compute(a) (3 points)limx!0x3-p9+x(b) (3 points) limx!⇡sinx⇡-x(c) (4 points) limx!-2x2-x-6x3+82
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8.Microtutorial(10 points) IfWdenotes the weight in pounds of anindividual, andtdenotes the time in months, thendW/dtis the rate ofweight gain or loss in lbs/mo. The current speed record for weight lossis a drop in weight from 487 pounds to 130 pounds over an eight-monthperiod. Show that the rate of weight loss exceeded 44 lbs/mo at sometime during the eight-month period.9. Letg(x) =(2x2-8x)23(a) (5 points) Find all critical points ofgover thex-interval [0,8].(b) (5 points) Find absolute maximum and absolute minimum ofgover [0,8].10. Lety=tan(x)(a) (5 points) Find the di↵erentialdyofy=tan(x) atx=⇡4.(b) (5 points) Use di↵erentials to find an approximate value fortan(0.885).Hint:⇡4⇡0.785.3
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