A. Write a function for your profits for each price you charge. This is done by multiplying (P-.5) times your function (y= -100x + 250). I.e. if your function is Cups Sold = 1000 - 100P, your profit function would be (P - .5)*(1000 - 100P). B. Calculate the first derivative of your profit function, and create another table
Data: regression equation: y= -100x + 250 regression coefficient: r= -1 X Y Predicted value 0.25 225 225 0.5 200 200 0.75 175 175 1 150 150 1.25 125 125 1.5 100 100 1.75 75 75 2 50 50 2.25 25 25 2.5
1. Give the definition of limit in three forms: ε?δ , graphical, and in your own words. 2. Define the derivative. List what you consider to be the five most useful rules concerning derivatives. 3. Give an argument for the product rule. 4. What is the tangent line approximation to a function? 5. What is the Taylor p
See the attached file. 71. The local game commission decides to stock a lake with bass. To do this 200 bass are introduced into the lake. The population of the bass is approximated by P(t) = 20 (10 + 7t)/(1 + 0.02 t) where t is time in months. Compute P(t) and P'(t) and interpret each. 57. The monthly sales of a new compute
If it costs Acme Manufacturing C dollars per hour to operate its golf ball division, and an analyst has determined that C is related to the number of golf balls produced per hour, x, by the equation C = 0.009x squared - 1.8x + 100. What number of balls per hour should Acme produce to minimize the cost per hour of manufacturing t
Volume. An open box is to be made from a six inch by six inch square piece of material by cutting equal squares from the corners and turning up the sides. Find the volume of the largest box that can be made Area. A rectangular page is to contain 36 square inches of print . The margins at the top and bottom and on each si
Find 3rd derivative f(x)= 3/16x^2 Find the indicated value f(x)= 9-x^2 value f''(-sq rt 5) Find f'''(x) f''(x)=2x-2/x Find the second derivative and solve the equationf''(x)=0 f(x)=x/x^2+1 The velocity of an object in meters per second is v(t)=36-t, 0<t<6 Find the velocity and acceleration of the
Find the derivative of the function g(x)=the integral as tan(x) goes to x^2 of dt/(sqrt(7+t^4)); g'(x)=___
A container with a rectangular base, rectangular sides and no top is to have a volume of 2 subic meters. The width of the base is to be 1 meter. When cut to size, material costs $20 per square meter for the base and $15 per square meter for the sides. What is the cost of the least expensive container?
1. Differentiate from first principles( for x radians): a) sin x b) cos x 2. Products and quotients For a function, f(x), which can be expressed as a product or quotient of other functions, u(x) and v(x), there exist a) the product rule, f(x) = u(x) ? v(x),
Problem: If y = tan^-1[(1+x)/(1-x)], find dy/dx. See the attached file.
Problem: Find the differential coefficient of sec(tan-1 x) with respect to x.
Use implicit differentiation to find dy/dx x^2 + 9xy + y^2=0 y^2 + x^2 - 6y - 2x - 5 =0
Given f(x)= sqrt x, find f''''(x) given f(x)= x^2 + 3/x, find f''(x) given f'''(x)= 20x^4 - 2/x^3, find f'''''(x).
G(t)= t/ (1 - t)^3 f(x)= (x^2 + 1/x)^5 f(x)= [(x - 2)(x +4)]^2 f(s)= s^3(s^2 - 1)^5/2 g(x)= (3x + 1)^2/ (x^2 + 1)^2
Find the derivative of the function and simplify. y= (3x^2 + 7) (x^2 - 2x) s= (4 - 1/t^2)(t^2 -3t) f(x)= x^2 + x - 1/ x^2 -1 f(x)=^3 sqrt(x^2 -1) g(x)= sqrt (x^6 - 12x^3 + 9)
Find the derivative of the function and simplify. y= (3x^2 + 7) (x^2 - 2x) s= (4 - 1/t^2)(t^2 -3t) f(x)= x^2 + x - 1/ x^2 -1 f(x)=^3 sqrt(x^2 -1) g(x)= sqrt (x^6 - 12x^3 + 9)
The weekly demand and cost functions for a product are p= 1.89 - 0.0083x and c= 21+ 0.65x write the profit function for this product. find the marginal cost of the function. C= 475 + 5.25x^2/3 find the marginal revenue function. R= x(5+ 10/ sqrt(x) Find the marginal profit function. P= 1/1
The position of the function of a particle is given by s= 1/t^2 + 2t + 1 where s is the height in feet and t is the time in seconds. Find the velocity and acceleration functions. use implicit differentiation to find dy/dx x^2 + 3xy +y^3 = 10.
Find the derivative of the function and simplify. f(x)= x^3(5 - 3x^2) f(x)= x^2 + x - 1/x^2 - 1 f(x)= (5x^2 + 2)^3 g(x)= x sqrt(x^2 + 1) given f(x)= 3x^2 + 7x +1, find f''(x)
A rock is dropped from a tower on the Brooklyn Bridge, 276 feet above the east river. Let t represent the time in seconds. a.) write a model for the position of the function (assume air resistance is negligible.) b.) find the average velocity during the first 2 seconds. c.) find the instantious velocity when t=2 and t
Use the definition of the limit to find the derivative of the function f(x) = 7x + 3 Find the slope of the graph of F at the indicated point f(x) = sqrt(x) + 2; (9,5) use the derivative to find the equation of the tangent line to the graph of f at the indicated point. f(x) = x^2 + 3/x; (1,4)
Find the derivative of the functions. y= (2x - 7)^3 h(x)= (6x - x^3)^2 f(t)= sqrt(t + 1) f(x)= x^3(x - 4)^2
Find the value of the derivative of the function at the indicated point. f(x)= 1/3 (2x^3 - 4) point (0, -4/3) h(x)= x/(x - 5) point (6,6) f(t)= (2t^2 - 3)/3t point (2, 5/6)
G(t)= 3t^2 / sqrt (t^2 + 2t - 1) The number N of bacteria in a culture after t days is modeled by: N= 400 [ 1- 3/ (t^2 + 2)^2] Complete the table. What can you conclude? t 0 1 2 3 4 dN/dt _ _ _ _ _.
Find the derivative of the functions. f(x)= x(3x - 9)^3 y= x sqrt(2x + 3) y= t^2 sqrt (t - 2)
Y= 4x^3/2 /x
Find the derivative of the functions. y= 1/ x-2 s(t)= 1/ t^2+ 3t- 1 f(x)= 1/ (x^2- 3x)^2 y= 1/ (sqrt x + 2).
Find the derivatives of the functions y=x^2 + 2x/x y=3x^2 - 4x/6x f(x)= 3^sqrt x (sqrt x + 3) f(x)= 3x- 2/2x - 3
4.) Ever wonder why bacteria are so hard to contain ? A certain coloney of bacteria has an initinal population of 10,000. After t hours, the coloney has grown to a number P(t) given by P(t) = 10000(1+.86t + t^2). a.) Find the growth rate (rate of change) of the population P with respect to time t. [FInd P'(t)] b.) Fi