Most popular questions and responses by Adam Janky
1. ## calculus

Suppose that the proportion P of voters who recognize a candidate's name t months after the start of the campaign is given by the following equation. (Round your answers to three decimal places.) P(t) = 11t t2 + 100 + 0.14 (a) Find the rate of change of P

2. ## calculus

The data entry speed (in entries per minute) of a data clerk trainee is represented by the following equation, where x is the number of hours of training he has had. S = 10 0.8x + 4 , 0 ≤ x ≤ 100 What is the rate at which his speed is changing and what

3. ## calculus

The number of units of weekly output of a certain product is represented by the equation shown below, where x is the number of workers on the assembly line. There are presently 68 workers on the line. Q(x) = 200x + 4x2 (a) Find Q'(x) and estimate the

4. ## calculus

Find the coordinates of points where the graph of f(x) has horizontal tangents. As a check, graph f(x) and see whether the points you found look as though they have horizontal tangents. f(x) = −x3 + 6x2 − 9x + 13 (x, y) = ( ? ) (smaller x-value) (x, y)

5. ## calculus

Consider the following. y = (2x2 + 5)(x3 − 25x) at (5, 0) (a) At the indicated point, find the slope of the tangent line. (b) Find the instantaneous rate of change of the function.

6. ## calculus

At the indicated point for the function, find the following. A graphing utility's numerical derivative feature can be used to check your work. y = (x3 + 2x)3 at x = 3 (a) Find the slope of the tangent line. (b) Find the instantaneous rate of change of the