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Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…
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- How are the absolute maximum and minimum similar to and different from the local extrema?Question no 1:- f(x) = x²- 6x² + 9x + 1 Question no 2:- f(x) = x³+ 3x² - 9x - 3 Question no 3:- f(x) = x⁴ - 8x³ + 18x² - 27 Determine all local optimum points and all inflection points. Please give the answer of these three question.False. For example, the maximum off (x) = x 2 + 1 on [l, 2] is 5, occurring at x = 2, but f' (2) # 0. (c) True (d) False. For example, the function f (x) = 2x 2 - x 3 has a single local minimum on [-1, 3], at x = 0, but the absolute minimum on [ -1, 3] occurs at the endpoint x = 3.
- find the extrema (minimum and maximum) of f(x) = x2-1 on (-1,2). If none, explain why.1) is it a convex function or a concave function? Explain 'why' in terms of the given equation. 2) does local minimum exist? yes/no?The curve enters the window in the second quadrant, goes down and right, and exits the window nearly vertical at the approximate point (−7.2, −3). The curve reenters the window nearly vertical at the approximate point (−6.7, −3), goes up and right becoming less steep, crosses the x-axis at x = −5, goes up and right becoming more steep, and exits the window at the point (−3.3, 3). The curve reenters the window nearly vertical at the approximate point (−2.9, 3), goes down and right, changes direction at the approximate point (−1.5, 0.5), goes up and right, and exits the window nearly vertical at the approximate point (−0.1, 3). The curve reenters the window nearly vertical at the approximate point (0.2, 3), goes down and right, changes direction at the approximate point (1.6, −2), goes up and right, changes direction at the approximate point (4.3, 2.7), goes down and right, and exits the window nearly vertical at the approximate point (5.8, −3). The curve reenters the window nearly…
- Q3: Find the critical points of the following function then test them for local maximum, local minimum and saddle point. f (x, y) = x3 + y3 - 3xy + 15The fourth interaction when the positive x-intercept of the y=f(x) is approximated by the interval Halving method with initial approximations x1=1 and x2=4, has maximum error smaller than 0.1875 analyse using the graph below to determine weather the above statement is true or falseThe oxygen supply, S, in the blood depends on the hematocrit, H, the percentage of red blood cells in the blood. If S = k(H) = aHe-bH for positive constants a and b, with domain (0, infinity) and k'(H) = ae-bH(1-bH) 1. Use the definition to find the only critical point H1 of k on its domain. 2. Use a number line and the first derivative test to show that the oxygen supply is maximised at H1.You have to explain how you determine the sign of the first derivative on every interval. 3. What is the maximum oxygen supply? 4. How does increasing the value of the constants a and b in the same proportion change the maximumvalue of S? Please answer 3 and 4
- 5x−12/x^2−x−42 has vertical asymptote(s) at x=ANSWER THE PROBLEM WITH COMPLETE SOLUTION (INCLUDE A TABLE) Using Direct Search Method, estimate the root of the function f(x) = e -x - x in four decimal places with interval [0,1], and with tolerance limit 0.0002Given the function: f(X)= x4-8x2-3a. What are the critical values? b.What are the open intervals on which the function is increasing and decreasing? (You must show your work) c. What are the Maximum/Minimum points (x,y) that occur according to your work? d. What are the x-values for the possible inflection points? e. What are the open intervals on which the function is concave up/concave down?(You must show your work) f. What are the Inflection Points (x,y) that occur according to your work?