71–74 - Graph of an Inverse Function A function f is given. (a) Sketch the graph of f. (b) Use the graph of f to sketch the graph of f'. (c) Find f!. 71. f(:) - Зх — 6 72. f(x) = 16 – x, x20 73. f(x) = Vx + I 74. f(x) = x' - 1
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- A cable hangs between two poles of equal height and 30 feet apart. Set up a coordinate system where the poles are placed at x=−15 and x=15, where x is measured in feet. The height (in feet) of the cable at position x is h(x) = 17cosh(x/17) where cosh(x) = (e^x+e^-x)/2 is the hyperbolic cosine, which is an important function in physics and engineering. The cable is ______ feet long?Using "Numerical Differentiation (Backward Finite Difference)" Problem Solving f(x) = 2cos (3x-2) with h = 0.002, What is f'(1) and f''(1)?5.2(5) PLEASE SHOW YOUR WORK STEP BY STEP!! With the function (shown in the image) Determines the first and second derivatives, then uses a variation array to organize the main characteristics of f (x).
- What does “composition of functions” mean? Give an example using two functions f(x) and g(x), along with new functions created by m(x) = f(g(x)) and k(x) = g(f(x)). Also show the derivative of m(x) and the derivative of k(x).Suppose the function f(x) has a domain of all real numbers except x = 5. The first derivative of f(x) is shown below. f '(x) = (-3(x-1)e8x)/((x-5)3) Find the interval(s) where f(x) is increasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) Find the interval(s) where f(x) is decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) Find the x-coordinates of all local extrema on the graph of f(x). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) Local Maxima at x = Local Minima at x =The point Q (-4,7) lies on the function f(x). Suppose f(x) is transformed according to: y=-3 f [0.5(x + 3)] + 5. Determine the x-coordinate of the transformed point, Q'. Enter only the x-coordinate, a single value, rounded correctly to 2 decimal places (ie 3.46 or 7.00 or 1.50)
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