Rules and Applications of the Derivative -------------------------------------------------------------------------------- 1. Use the Product Rule to find the derivatives of the following functions: a. f(X) = (1- X^2)*(1+100X) b. f(X) = (5X + X^-1)*(3X + X^2) c. f(X) = (X^.5)*(1-X) d. f(X) = (X^3 + X^4)*(30
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
The second derivative of a function is given as: f"(x) = 12x-1 At the point (-2,7) the tangent to the function is given by: y=kx-3 Find the function f(x).
Find dy/dx y = 2x^3+6x^2+6x+4
Differentiate each of the following functions with respect to the independent variable, use the above worked examples as an example: Please see the attached file for the fully formatted problems.
Find the first derivative 1.) f(x)=e^-1/x^2 2.) f(x)= (x^2+1)e^4x 3.) y=xe^x- 4e^-x Find the second derivtive 4.)f(x)=2e^3x+3e^-2x
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
What are the steps for finding the derivative? 2x + 512/x
The math department is planning to build a park for calculus students along the riverbank. The park is to be rectangular with an area of 512 square yards and is to be fenced off on the three sides not adjacent to the river (draw a picture) a.) What is the least amount of fencing required for this job? b.) How long and
The Happy Hound Haven Company estimates that the revenue (in dollars) from the sale of x doghouses is given by R(x)= 625+.03x+.0001x^2. Approximate the change in revenue from the sale of one more doghouse when 1000 doghouse are sold. (Make sure to do this using derivatives). Am I correct? The derivative is R'(x) = 0.03+0.00
For several weeks , campus security has been recording the speed of trafic flowing past a certain intersection on campus. The data suggests that between 1:00 and 6:00 pm on a normal weekday, the speed of the traffic at the intersection is approximately S(t)=t^3-10.5t^2+30t+20 miles per hour, where t is the number of hours past
Find the extrema of the function f(x)=x^3-x^2-x+2 on the closed interval [0,2] Find two numbers whose product is 192 and the sum of the first plus three times the second is a minimum. (there should be a primary and a secondary equation)
Find the number of units x that produce a maximum revinue R. R=800x-0.2x^2 R=48x^2-0.2x^3 Find the number of unites x that produce the minimum average cost per unit C. C=1.25x^2+25x+8000 C=0.001x^3+5x+250 find the amounts of advertising that maximizes the profit P. (s and p are measeured in thousands
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
Let and let C be the circle , . A. Compute Note: Your answer should be an expression of x and y; e.g. "3xy - y" B. Compute Note: Your answer should be an expression of x and y; e.g. "3xy - y" C. Compute Note: Your answer should be a number Please see the attached file for the fully formatted proble
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