Lecture 6 : Derivatives and Rates of Change. In this section we return to the problem of finding the equation of a tangent line to a curve, y = f(x).

Find the rate at which the volume of the cone is increasing, when the radius of the base of the cone has reached 2.5 cm . (You may assume that the bolt is ...

This chapter ends with practice in some traditional problems involving differentiation. Follow through these worked examples and then attempt Exercise 8G.

(b) Estimate the instantaneous rate of change at noon. SOLUTION. (a) (i) From noon to 3 P.M. the temperature changes from 14.3°C ...

To estimate the slope of the tangent at use two points and the difference quotient. For one point, use the point where you want the tangent line to be.

The purpose of this Collection of Problems is to be an additional learning resource for students who are taking a differential calculus course at Simon ...

For each problem, find the instantaneous rate of change of the function at the given value. 1) y = x. 2 - 2x + 1; 2. A) 0. B) -. 1. 2. C) 4. D) 2.

This is a set of exercises and problems for a (more or less) standard beginning calculus sequence. While a fair number of the exercises involve only routine ...

Example 1.3 Find the equation of the line through (2,3) which is perpendicular to the line L : 2x + 3y = 11. For the general curve given by the equation y = f ...

Calculus Related Rates Problems Worksheet. 1) An 8-foot ladder is leaning against a wall. The top of the ladder is sliding down the wall at the rate of 2.