1 / 10

Applied Calculus (MAT 121) Dr. Day Monday, March 19 , 2012

Applied Calculus (MAT 121) Dr. Day Monday, March 19 , 2012. Derivatives of Exponential Functions(5.4 ) and Log Functions (5.5) Remember Your Derivative Rules! Derivative Rule for Exponential Functions Derivative Rule for Logarithmic Functions Using and Applying these Derivatives.

griffin-duffy
Télécharger la présentation

Applied Calculus (MAT 121) Dr. Day Monday, March 19 , 2012

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Applied Calculus (MAT 121)Dr. Day Monday, March 19, 2012 Derivatives of Exponential Functions(5.4) and Log Functions (5.5) • Remember Your Derivative Rules! • Derivative Rule for Exponential Functions • Derivative Rule for Logarithmic Functions • Using and Applying these Derivatives MAT 121

  2. Exponential Functions Big Ideas • What are Exponential Growth and Exponential Decay? • What sort of applications use exponential functions as their mathematical models? • What algebra do we need to remember to work with exponential functions? • How do we undo exponentiation? We need the inverse function, called the logarithm function. • Where does calculus fit in to all of this? MAT 121

  3. Compound Interest Periodic Compounding • A: amount in account • P: amount of original deposit (principal) • i: annual interest rate, expresses as a decimal value • n: number of compounding periods per year • t: number of years the principal remains in account Continuous Compounding • A: amount in account • P: amount of original deposit (principal) • r: annual interest rate, expresses as a decimal value • t: number of years the principal remains in account MAT 121

  4. Review: Derivative Rules • Power Rule • Product Rule • Quotient Rule • Chain Rule MAT 121

  5. Derivatives of Exponential Functions • For y = ex: • For y= kex: • For y= eu(x): MAT 121

  6. Derivatives of Exponential Functions y= ex y= 3ex y= e-2x y= 5x3 + e5x y= (1+e2x)/(e-3x-x) MAT 121

  7. Using These Derivatives • Determine all intervals where the function f(x) = x2e-x is increasing and where it is decreasing. • Find the absolute extrema of the function. h(x) = ex2 - 4 on [-2,2]. • The percentage of alcohol in a person's bloodstream thrs after drinking 8 fluid oz of whiskey is modeled by the equation. A(t) = 0.29te-0.3t, 0 ≤ t ≤ 12. How fast is the percentage of alcohol in a person's bloodstream changing after 1/2 hr? After 5 hr? Round your answers to four decimal places. MAT 121

  8. Derivatives of Logarithmic Functions • For y =ln(x): • For y= kln(x): • For y=ln(u(x)): MAT 121

  9. Derivatives of Logarithmic Functions y= ln(x) y= ln(3x) y= x2ln(3x-1) y=e5xln(5x) y= (ln(3x))/(3ln(x)) MAT 121

  10. Assignments WebAssign 5.4 due tonight! 5.5 due Wednesday night 5.6 due Thursday night Test #4: Friday, March 23, 2012. MAT 121

More Related