Differential And Integral Calculus By Feliciano And Uy Chapter 4
Chapter 4
In many standard calculus textbooks used in the Philippines (such as Feliciano and Uy), typically marks the transition from basic differentiation rules to Applications of Derivatives . This chapter is crucial as it connects abstract mathematical rules to solving real-world problems involving motion, optimization, and curve analysis.
- Tangent Line: The tangent to a curve at a given point is the line that just touches the curve at that point, with the same slope as the curve.
- Normal Line: The normal to a curve at a point is the line perpendicular to the tangent at that point.
Example (from Feliciano & Uy, typical problem):
Find the equations of tangent and normal to (y = x^2 - 4x + 3) at (x = 2). Solution : Chapter 4 In many standard calculus textbooks used
- Identify what is to be maximized/minimized.
- Express it as a function of one variable.
- Differentiate, set (f'(x) = 0).
- Check if max/min (first or second derivative test).
- Answer in a sentence with units.
Inverse Trigonometric Functions
: Finding derivatives for functions like , and others. Tangent Line: The tangent to a curve at
