Applications of derivative: Surface and volume
A company is constructing an open-top, square-based, rectangular metal tank that will have a volume of 66 ft^3. What dimensions yield the minimum surface area? Round to the nearest tenth, if necessary.
Derivatives
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Use analytic methods to find the extreme values of the function
Use analytic methods to find the extreme values of the function on the interval and where they occur. 15. f(x) = sin (x + pi/4), 0<x<7pi/4 16. g(x) = sec x, -pi/2<x<3pi/2 ---
Derivatives : Point of Horizontal Tangent and Derivative at a Point
Consider the curve given by x^2+4y^2 = 7 + 3xy a) Show that there is a point P with x-coordinate 3 at which the line tangent to the curve at P is horizontal. Find the y-coordinate of P. b) Find the value of d^2*y/d*x^2 at the point P found in part a).
Derivatives : Speed of shadow - A tightrope is stretched 30 ft above the ground between Building 1(at point A) and Building 2( point B), which are 50 ft apart. A tightrope walker, walking at a ...
A tightrope is stretched 30 ft above the ground between Building 1(at point A) and Building 2( point B), which are 50 ft apart. A tightrope walker, walking at a constant rate of 2 feet per second from point A to point B, is illuminated by a spotlight 70 feet above point A. a) how far from point A is the tightrope walker when
Rate of travel along a curve with respect to the x-axis.
As a particle travels along the curve y=x^(3/2) its distance from the origin is increasing at a rate of 11units/sec. At what rate is the particle traveling with respect to the x-axis at the moment that the x-coordinate of the particle is 3? Choices are: A. 3.5, B. 4, C. 4.5, D. 5, E. 5.5 Please show work.
Derivative Explanation Comprised
(See attached file for full problem description) --- Show all steps in finding the derivative of: f(x) = sin2(pi)x state which rule(s) were used. ---
Find the derivative of sin^5(x^3).
Find the derivative of: [state which rules you used] sin^5(x^3) ---
Lagrange multipliers and Strirling's approximation
See attached file.
Application of Rolle's Theorem for Closed Interval
Please solve the problem to the specified answer and please provide as much explanation of each step as possible. Determine whether Rolle's Theorem can be applied to f on the closed interval [a,b]. If Rolle's theorem can be applied, find all values of c in the open interval (a,b) such that f'(c) = 0. f(x) = x^2 - 2x - 3/x
Differentiation: Finding the Derivative
In solving the problem, it is determined that the derivative of h(x) = sin^2x + cosx. 0 is less than x which is less than 2pi was: h'(x) = cosxsinx +sinxcosx - sinx which then simplified to 2sinxcosx-sinx which then simplified to sinx(2cosx-1) When do the derivative, I get cos^2x -sinx Would you explain what I a
Differentiation Explanation Solved
Please solve the problem to the specified answer and please provide as much explanation as possible. f(x) = x^2logsub2(x^2 +1) x = 0
Applications of Derivatives Word Problem
A plane flying with a constant speed of 24 km/min passes over a ground radar station at an altitude of 9 km and climbs at an angle of 40 degrees. At what rate is the distance from the plane to the radar station increasing 3 minutes later?
Applications of Derivatives Word Problems : At noon, ship A is 30 nautical miles due west of ship B...
At noon, ship A is 30 nautical miles due west of ship B. Ship A is sailing west at 17 knots and ship B is sailing north at 19 knots. How fast is the distance between the ships changing at 4 PM, in knots? (You have to use all data provided.)
Assistance with Finding the Derivatives
Find f'(x)=? (derivatives) (a) f(x) = 7ln(cosx) (b) f(x) = 15 x^(lnx).
Rate of Change in Speed and Distance
(1) At noon, ship A is 60 nautical miles due west of ship B. Ship A is sailing west at 19 knots and ship B is sailing north at 25 knots. How fast is the distance between the ships changing at 8 PM, in knots? (2) A street light is at the top of a 22 ft tall pole. A woman 12 ft tall walks away from the pole with a speed of 9 f
Determining the Local Extrema
Determine the local extrema of the following function: (-2/3x^3)-(21/2x^2)-5x+8.
Continuous Function on an Open Interval
Please explain why a continuous function on an open interval may not have a maximum or minimum. Please illustrate explanation with a sketch of the graph of a function.
Key data regarding differentiation
Explain whether each statement is true or false. Please give short explanation why and if false, please give an example. a) The maximum of a function that is continuous on a closed interval can occur at two different values in the interval. b) If a function is continious on a closed interval, then it must have a minimum
Differentiation
Please locate the absolute extrema of the function (if any exist) over the indicated intervals. Please show steps so I can follow. Thanks. Please solve using the following general method: Find derivative. Use derivative to find critical numbers. Use f to evaluate critical numbers and end points to find absolute extrema.
Derivatives and Rate of Change : Rate of Increasing Area of an Isoceles Triangle
Let θ (theta) be the angle between equal sides of an isosceles triangle and let x be the length of these sides. If x is increasing at ½ meter per hour and θ (theta) is increasing pi/90 radians per hour, find the rate of increasing of the area when x=6 and θ=pi/4.
Partial Derivatives : Find fxy(1,pi/2) for f(x,y)=sin((x^2)y).
Find fxy(1,pi/2) for f(x,y)=sin((x^2)y). Please see the attached file for the fully formatted problems.
Directional Derivative and Maximum Rate of Increase
Find the directional derivative of the function f(x,y)=3x2-y2+5xy at the point P(2,-1) in the direction of a=(-3i-4j). Also find the maximum rate of increase of f(x,y) at P.
Differentiation : Locate the absolute extrema of the function
Please locate the absolute extrema (maxima and minima) of the function (if any exist) over the indicated intervals. 38. f(x) = √(4 - x^2) (a) [-2,2] (b) [-2,0] (c) [-2,2] (d) [1,2] Please solve using the following general method: Find derivative. Use derivative to find critical numbers. Use f to evaluate c
Differentiation, extrema of a function
Please show the how to solve the following. Please offer as much explanation as possible. Thanks. Graph a function on the interval [-2,5] having the following characteristics: Critical number at x = 0, but no extrema Absolute minimum at x = 5 Absolute maximum at x = 2
Differentiation and Locating Absolute Extrema of Function
Locate the absolute extrema of the function on the closed interval. f(x) = -x^2 + 3x [0,3] Answer: Minimum: (0,0) and (3,0) Maximum: (3/2, 9/4).
Derivative of the Inverse of a Function at a Point
Let f(x) = x^3 -7x^2 + 25x -39 and let g be the inverse function of f. What is the value of g'(0)? Please show how to solve to the answer of 1/10
Derivatives: Tangents and Differentiation
Consider the relation defined by the equation tan y = x + y for x in the open interval 0 is less than or equal to x which is less than 2pi (a) Find dy/dx in terms of y (b) Find the x- and y- coordinate of each point where the tangent line to the graph is vertical (c) Find d^2y/dx^2 in terms of y
Derivatives
Please show how to solve to the answer of 1/2 If f(x) = x-1/x +1 for all x not equal to -1, then f'(1) =
Find Equation of Curve Given the Equation of a Tangent
If y = 4x + 3 is tangent to the curve y = x^2 + k, then k is: Please show how to solve to the answer of 7.
Derivatives : Find Derivative from a Table of Values
Using the table of information for differentiable functions f(x) and g(x) at x = 2 and x=3, determine the derivative below. Chart: x f(x) g(x) f'(x) g'(x) 2 3 5 -2 -3 3