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Lecture

# Section 2.1 - The Tangent and Velocity Problem

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University of Massachusetts Amherst

Mathematics

MATH 131

John Gambino

Fall

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2.1 – The Tangent and Velocity
Problem
The derivative is:
The instantaneous rate of change of a function f(x) with respect to x at x=a
The slope of the tangent line to the curve y=f(x) at x=a
The limit of the difference quotient: ( ) ( )
The slope of y=f(x) at x=a
The secant line finds the average rate of change whereas the tangent line finds the
instantaneous rate of change
1. Find the equation of the tangent line to the parabola at the point P(1, 1).
x , ,
2 4
1.5 2.25
1.1 1.21
1.001 1.002001
**ON AN EXAM LEAVE IN POIN

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