### Differentiation

Please state whether each statement is true or false, and if false please explain why The maximum slope of the graph of y = sin(bx) is b If f''(2) = 0, then the graph of f must have a point of inflection at x = 2.

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Please state whether each statement is true or false, and if false please explain why The maximum slope of the graph of y = sin(bx) is b If f''(2) = 0, then the graph of f must have a point of inflection at x = 2.

Please solve and explain to the specified answer. Please explain solution. The deflection D of a particular beam of length L is D = 2x^4 - 5Lx^3 + 3L^2x^2 where x is the distance from one end of the beam. Find the value of x that yields the maximum deflection.

Please sketch a graph of a function f have the indicated characteristics. Please explain. (a) f(0) = f(2) = 0 f'(x) > 0 if x <1 f'(1) = 0 f'(x) < 0 if x > 1 f''(x) < 0 (b) f(0) = f(2) = 0 f'(x) < 0 if x < 1 f'(1) = 0 f'(x) > 0 if x > 1 f''(x)

S represents weekly sales of a product. What can be said of S' and S'' for each of the following? (a) the rate of change of sales is increasing (b) sales are increasing at a slower rate (c) the rate of change of sales is constant (d) sales are steady (e) sales are declining, but at a slower rate (f) sal

Please solve the following. All explanation is welcome. Consider a function f such that f' is decreasing. Sketch graphs of f for (a) f' is less than zero and (b) f' is greater than zero.

Please solve and offer explanation for the following: A differentiable function f has one critical number at x = 5. Identify the relative extrema of f at the critical number if f'(4) = -2.5 and f'(6) = 3.

Please show how to solve the problem to the specified answer. Please offer as much explanation as possible. Coughing forces the trachea to contract, which affects the velocity v of the air passing through the trachea. Suppose the velocity of the air during coughing is v = k(R - r)r^2, 0 is less than or equal to r w

The function f is differentiable on the interval [-1,1]. The table shows the values of f' for selected values of x. Sketch the graph of f, approximate the critical numbers, and identify the relative extrema. x -1 -0.75 -0.50 -0.25 f'(x) -10 -3.2 -0.5 0.8 x 0 0.25 0.50

Please indicate if each statement is true or false and if false please explain why If the graph of a function has three x intercepts, then it must have at least two points at which its tangent line is horizontal. If f'(x) = 0 for all of x in the domain of f, then f is a constant function.

(See attached file for full problem description with proper equations) --- First: solve these problems. Second: check my answers (they're not simplified). Third: if my answers are wrong explain why. Find . My Answers: 1. y = (x3 + 1)20 2. y = (x3 + y3) 20 ---

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. Thanks. 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 -

In solving the problem on Posting Number 55676 a few minutes ago, the brainmass tutor 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 deriv

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

Find f'(x)=? (derivatives) (a) f(x) = 7ln(cosx) (b) f(x) = 15 x^(lnx)

Determine the local extrema of the following function: (-2/3x^3)-(21/2x^2)-5x+8 Thank you!

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

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 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