MTH 1321 Chapter Notes - Chapter 3: Constant Function, Trigonometric Functions, Difference Quotient

• School: Baylor University
• Department: Mathematics
• Course: MTH 1321
• Professor: Steven Cates

Document Summary

Difference quotient= f(a+ h)- f(a)/ h: derivative: the limit of the difference quotients (if it exists) When limit exists, we say that f is differentiable at a. Tangent line: assume that f is differentiable at a. the tangent line to the graph of y= f(x) at p= (a, f(a)) is the line through p of slope f"(a) If f(x)= mx + b is a linear function, then f"(a)=m for all a. If f(x)= b is a constant function, then f"(a)=0 for all a: estimating the derivative. Approximations to the derivative are useful in situation where we cannot evaluate exactly. The derivative is the limit of difference quotients, the difference quotient should give a good numerical approximation when h is sufficiently small.