8. MicrotutoriātIf W denotes the weight in pounds of anindividual, and t denotes the time in months, then dW / dt is 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 – 8a)³%3D(a)Find all critical points of g over the x-interval (0,8].(b)over 0, 8].Find absolute maximum and absolute minimum of gWhen treating cancer, it is an advantage to know the rate ofgrowth of the cancer tumor. A mathematical model for cancer growthshows that when the diameter of a particular spherical tumor is 16 mm,10.it is growing at a rate of 0.4 mm a day. How fast is the volume of thetumor changing at that time?3-2XAXYf(x) = BVABflx)=3x-x2F(xtn) = 3(x-h) -(x-)*(x)(3X-X2)214-X)-(31x2/kYran-lY-h)2 -36 +x 2

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Step 1

To determine:

Part a) The critical points on the interval [0, 8].

Part b) Absolute maximum and minimum on the interval [0, 8].

Step 2

Given:

Step 3

Part a)

Compute critical points of ...

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MathCalculus