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.
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.
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 ---
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).
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
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.
(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: [state which rules you used] sin^5(x^3) ---
See attached file.
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
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
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
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?
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.)
Find f'(x)=? (derivatives) (a) f(x) = 7ln(cosx) (b) f(x) = 15 x^(lnx).
(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
Determine the local extrema of the following function: (-2/3x^3)-(21/2x^2)-5x+8.
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.
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
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.
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.
Find fxy(1,pi/2) for f(x,y)=sin((x^2)y). Please see the attached file for the fully formatted problems.
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.
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
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
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).
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
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
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) =
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.
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