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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Asked Dec 10, 2019
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8. Microtutoriāt
If W denotes the weight in pounds of an
individual, and t denotes the time in months, then dW / dt is the rate of
weight gain or loss in lbs/mo. The current speed record for weight loss
is a drop in weight from 487 pounds to 130 pounds over an eight-month
period. Show that the rate of weight loss exceeded 44 lbs/mo at some
time during the eight-month period.
9. Let
g(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 g
When treating cancer, it is an advantage to know the rate of
growth of the cancer tumor. A mathematical model for cancer growth
shows 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 the
tumor changing at that time?
3-2X
AXY
f(x) = BVAB
flx)=3x-x2
F(xtn) = 3(x-h) -(x-)*
(x)
(3X-X2)
214-X)-(
31x
2/k
Yran-lY-h)2 -36 +x 2
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8. Microtutoriāt If W denotes the weight in pounds of an individual, and t denotes the time in months, then dW / dt is the rate of weight gain or loss in lbs/mo. The current speed record for weight loss is a drop in weight from 487 pounds to 130 pounds over an eight-month period. Show that the rate of weight loss exceeded 44 lbs/mo at some time during the eight-month period. 9. Let g(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 g When treating cancer, it is an advantage to know the rate of growth of the cancer tumor. A mathematical model for cancer growth shows 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 the tumor changing at that time? 3-2X AXY f(x) = BVAB flx)=3x-x2 F(xtn) = 3(x-h) -(x-)* (x) (3X-X2) 214-X)-( 31x 2/k Yran-lY-h)2 -36 +x 2

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Expert Answer

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:

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8 (x)=(2x² -8x 2.r -8.x

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Step 3

Part a)

Compute critical points of ...

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8(x)=(2x² -8x) 8(*) = (2* - 8r)5 -(2.x² – 8x) dx dx -(2x² – &r) dx (2x² – 8x 3 - 8x (2r - 8x)*(4x -8) (2x* – &r)*(4. (x– 2)(2x² – &r) 3 g'(x)=0=(x- 2)(2r² - 8r) =(x-2)(2r² - &x) = (x– 2) %3D 2x Vx- 4 Critical points of the function are x = 0,2,4.

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Tagged in
MathCalculus

Functions