Q.3 If ƒ(x)=-Vr-2Find(x*-x+1)*(a) The intervals on which f is increasing,(b) The intervals on which f is decreasing,(c) The open intervals on which f is concave up,(d) The open intervals on which f is concave down, and(e) The x-coordinates of all inflection points

Note: Given function is fx=x-2x2-x+12 The domain is 2,∞ a. Differentiate both sides,…

Answered: Q.3 If f(x)= √x-2 2 (x² − x + 1)² Find…

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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A function r(x) passes through the points as shown in the table to 123 5678| 11 the right. Which of the following could be a midpoint r(x) | a bc def8h 11 approximation to |r(x)dx I. 2b+8f П. 4с + 68 II. 10е A. I only В. П only C. III only D. I, II, and III
4. Let f(x) := r³ – 15x + 1. (a) Use the Intermediate Value Theorem to prove that f(x) has a root on the interval [-4,–3]. (b) Prove that ƒ has three real-valued roots. (Hint: You do not want to try and factor this or find the exact roots. Simply show that they exist.)
2. Consider the function f(x) = 4 – x². (a) Draw a sketch of the graph of the function. (b) Find the slope of the secant line connecting the points P(1, 3) and Q(2,0) on the graph. (c) Find the slope of the secant line connecting the points P(1,3) and Q(x,4 – x²). (d) Use algebra to simplify your formula from part (c) as much as possible, assuming that P and Q are distinct points. (e) What value do you get when you plug x = 1 into the simplified expression you found in part (d)? (f) Assume that your answer in part (e) is the slope of the tangent line to the graph y = 4 – x2 at the point P(1,3). Use that information to write an equation for the tangent line to the graph y = 4 – a² at the point P(1,3).
c) Find the vertical intercept, or intercepts, of the function v(t) given below. v(t) = 4|t – 5| – 12 Give your answer(s) as a coordinate point(s) (like (- 3, 1)) in the box given below. If there is more than one vertical intercept, give all possible answers separated by commas.
7. Which function(s) have/has a zero at x = -5? a. y = 2*+5-1 b. y = x2 -5 C. y = |x - 5| d. y = (x + 5)(x - 9)
1. [K&U/5] Determine the domain and range and explain which of the following relation is a function or not a function a) f(x) = 2x + 41 b) y = - x + 2

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Q.3 If f(x)= √x-2 2 (x² − x + 1)² Find (a) The intervals on which f is increasing, (b) The intervals on which f is decreasing, (c) The open intervals on which f is concave up, (d) The open intervals on which f is concave down, and (e) The x-coordinates of all inflection points