Find critical number(s) and inflection point(s) on the curve:\[ y = x - 9 \ln x - \frac{18}{x} \quad \text{where} \quad x > 0. \]Use the second derivative to classify the critical points and give intervals where the function is increasing/decreasing and also intervals where the function is concave up/concave down.

Let us consider the function y=f(x) Point of inflection is the obtained by d3ydx3=0 The function is…

Answered: 4. Find critical number(s) and…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Sketch the curve of f(x), a function whose first derivative has the following properties. You must explain what each piece of information tells you about f(x). Make sure your sketch is labeled clearly with all important points. To be clear - you are sketching f(x), not f'(x). -4 1. f'(x) decreases when ï 1/3 5. f'(x) is negative when −3 < x < 1/ 13
There is strong evidence that the first level of processing what we see is done in the retina. It involves detecting something called edges or positions of transitions from dark to bright or bright to dark points in images. These points usually coincide with boundaries of objects. To model the edges, derivatives of functions such as f(x) = 1 e-ax, x ≥ 0 eax 1, x ≤0 need to be found. Use the central divided difference approximation of the first derivative of f(x) to calculate the functions derivative at x = 0.5 for a = 0.24. Use a step size of Ax = 0.125. Express your answer up to five (5) decimal places. Present your solution in your answer sheets.
3. Estimate the derivative using forward finite divided difference applying both truncated and more accurate formula using xi = 0.5 and step sizes of h1 = 0.25 and h2 = 0.125 f(x) = 12 + xex
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The critical number/s of the first derivative and the second derivative of a function must be determined to sketch the graph of the function. Select one: True False

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4. Find critical number(s) and inflection point(s) on the curve 18 y = x-9 lnx - where x > 0. x Use the second derivative to classify the critical points and give intervals where the function is increasing/decreasing and also intervals where the function is concave up/concave down.