DA with Derivatives

Math 31 Derivative Assessment

Complete a newspaper, newsletter, pamphlet, or any informational item showing how Calculus can be used in real life applications.

Your product must demonstrate your knowledge of:

·         Use of the product rule by taking the derivative of the product of two functions, both which have a minimum of 2 terms and are at least degree 2.

·         Use of the quotient rule by taking the derivative of a quotient of two functions, both which have a minimum of 2 terms and are at least degree 2.

·         Implementing the chain rule while taking the derivative.

·         Taking the derivative of a function which must use the combination of two or more of the following:

o   Chain Rule

o   Product Rule

o   Quotient Rule

·         Taking the derivative of a function which requires implicit differentiation. 

In addition, you must also:

·         Determine the slope at a point of a function.

·         Determine the equation of a tangent line of a function at a point.

·         Determine the second derivative of a function.

The work, determining the derivative and other answers can be supplied separate to your final product, but the solutions MUST make sense in the story, or scenario, you have placed them in.

Examples:

Recently the police has determined the crime rate of Red Deer can be shown by the function, c(d) = d^2, where c(d) is the amount of crimes committed on a day, and d is the day of the year.  This function applies to only the first 5 days of the year, then the function changes.  The rate of change of crime from day to day can then be demonstrated by the function c'(d)=2d, and the exact rate of change on the 3^rd day is 6 more crimes each day.

Sylvan lake was under attack, last night, by a mob equipped with catapults.  The height of one of the arms of a catapult, in meters, could be represented by the function h(t) = -t^2+9, where t is from 3 seconds before the arm reaches its maximum height to 3 seconds after it reaches it maximum height.  If the catapult launches its projectile at t = -2, the slope of the projectile would be 4 m/s and an acceleration of    -2 m/s^2 with an equation of 5(x+1)=y-5