Differential And Integral Calculus By Feliciano And Uy Chapter 4

Problem (Inspired by Chapter 4): A spherical balloon is inflated at a rate of ( 10 \text cm^3/\texts ). How fast is the radius increasing when the radius is ( 5 \text cm )?

Solution:

The authors begin by establishing the rules governing the interaction between derivatives and basic arithmetic operations. These theorems form the bedrock of differential calculus. Problem (Inspired by Chapter 4): A spherical balloon

Key Formulas:

Example (from Feliciano & Uy, typical problem):
Find the equations of tangent and normal to (y = x^2 - 4x + 3) at (x = 2).
Solution: Example (from Feliciano & Uy, typical problem): Find

Test:

Procedure:

Example:
(f(x) = x^3 - 3x)
(f'(x) = 3x^2 - 3 = 3(x-1)(x+1))
Critical points: (x = -1, 1)
Sign:

Example: ( y = \sin(5x^2) )

For time rates and optimization, you cannot solve what you cannot see. Spend 2 minutes drawing the ladder, the cone with water, or the rectangle inscribed in a semicircle. Label every variable.

Example: ( y = x^2 \tan x )