Ch 4. The Mean Value Theorem Multimedia Engineering Math Maximum & Minimum Rolle'sTheorem Mean ValueTheorem MonotonicFunctions First DerivativeTest Concavity &Inflection SecondDerivative Test
 Chapter 1. Limits 2. Derivatives I 3. Derivatives II 4. Mean Value 5. Curve Sketching 6. Integrals 7. Inverse Functions 8. Integration Tech. 9. Integrate App. 10. Parametric Eqs. 11. Polar Coord. 12. Series Appendix Basic Math Units Search eBooks Dynamics Fluids Math Mechanics Statics Thermodynamics Author(s): Hengzhong Wen Chean Chin Ngo Meirong Huang Kurt Gramoll ©Kurt Gramoll

 MATHEMATICS - CASE STUDY Introduction Liver Implant Assist Device While testing the energy generated by a liver implant assist device, Diana lost her research data because of computer crash. She saw a work formula on a piece of paper and wonders if this is the work function of the device. What is known: The expression of the liver implant assist device is w(t) = 17 - 15t + 9t2 - t3 The unit for work, power and time is mJ (mil-Joules), mw (mil-watts), and year respectively. The liver implant assist device needs to have positive energy generating rate (power) when the device starts to work. Questions Can this formula be the work function of liver implant assist device? Approach Using test for monotonic functions to find the functions increasing interval. The derivative of the energy function is energy generating rate (power).