MATH 140 Lecture 6: Derivatives

• School: PSU
• Department: Mathematics
• Course: MATH 140
• Professor: Chopra, Parsons

Document Summary

Definition: the tangent line to the curve y=f (x) at the point p(a,f (a)) is the line through p with slope m= lim x a f (x) f (a) x a given that this limit exists. The slope of the tangent line may be referred to as the slope of the curve at the point. Given the secant line pq , if h=x a then x=h+a and h approaches 0 if and only if x approaches a , then the slope of that secant line pq becomes mpq= f (a+h) f (a) h. Thus, the definition of a tangent becomes m= lim h 0 f (a+h) f (a) h. = f (a+h) f (a) h velocity ( instantaneous velocity)=v(a)= lim h 0 f (a+h) f (a) h. Derivatives t=a is equal to the slope of the tangent line at p.