AP Calculus Unit 4 Contextual Applications of Differentiation

University:
Whitman College
Course:
MATH-125 | Calculus I
Academic year:

2022
Views:

418

Pages:

1
Author:

conget2w7

Unit 4: Contextual Applications of Differentiation ● L’hopital’s Rule: If the function is differentiable and equals 0/0 or infinity/infinity, then the limit can be found by taking the derivative of the numerator function over the derivative of the denominator function. ○ ***Note that the derivatives of the numerator and denominator functions are taken independently of each other. ● Velocity, Acceleration, Position ○ The derivative of a position function gives you the velocity function. ■ Speed would be the absolute value of the derivative of a position function. ○ The derivative of a velocity function gives you the acceleration function. ● Related Rates: solving real life problems using derivatives ○ 1) Find the equation of the volume, according to the problem. ■ Ex.: A cube would be x³ ○ 2) Take the implicit derivative of the function with respect to time ■ Dy/dt or dx/dt o 3) Plug in the values given to you from the equation o 4) Solve.