question 12 please (e) Find the local maximum and local minimum.(f) Find the inflection points.(g) Graph the function y = f(x), clearly labeling all the values that youfound above. 12. The function f(x) and its first and second derivatives are as given below.f(x) = 1-2²₁(a) Domain of f(x) is(b) y-intercept isf'(x) = 23²(c) Horizontal asymptote(s) is.(d) Vertical asymptote(s) isand x-intercept is(e) Find the local maximum and local minimum.6-2xTA

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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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The 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
3. The function f(x) = x^4 − 4x^3 + 8x has a critical point at x = 1.(a) Find f"(x). (b) Then use the second derivative test to identify the critical point as eithera local minimum, a local maximum, or neither.
a) On the number line, mark the critical value(s) of f(x) and the sign of the first derivative between them as obtained from the graph. b) Where is f(x) increasing on it's domain? c) Where is f(x) decresing on it's domain? e) At what x-value(s) would f(x) have a relative maximum? d) At what x-value(s) would f(x) have a relative minimum?
11. Let h(x) = x^4 − 2x^2 + 3.(a) Find all critical points and use the First Derivative Test to characterize each as a local maximum, local minimum, or neither.(b) Use the Second Derivative Test to check your answers.(c) Find all inflection points.
1. A critical number of f′(x) is an inflection point of f(x).True or False 2. If the radius of a circle is increasing at a constant rate, then so is the circumference.True or False 3. If two variables x and y are functions of t and are related by the equationy = 1 −x^2, then dy/dt = −2x.True or False 4. When finding the global minimum of a function on an interval, you must usethe first or second derivative test to verify that your point is a global minimum.True or False
On the graph of f(x)=sinx and the interval [−2π,0), for what value of x does f(x) achieve a minimum?
1) Use the definition of a derivative to find f'(x) and f"(x), when f(x) = 2/x. I got f'(x) = -2/x2, but I am confused on how to get f"(x). 2) If a rock is thrown upward on Mars with a velocity of 15 m/s, its height in meters after t seconds is given by h=15t - 1.86t2. I need help starting this problem 3) lim (x--> inf) arctan(x2-x7) I need help starting the problem
2. f(x) = x^3 − 27x (a) Use the derivative of the function f(x) to find all critical points. (b) Draw and use a graph to classify each critical point of f(x) as a local minimum, local maximum, or neither.
Discuss the extreme-value behavior of the function ƒ(x) = x sin (1/x), x ≠ 0. How many critical points does this function have? Where are they located on the x-axis? Does ƒ have an absolute minimum? An absolute maximum?
Suppose that the first derivative of y = ƒ(x) is y' = 6(x + 1)(x - 2)2. At what points, if any, does the graph of ƒ have a local maximum, local minimum, or point of inflection?
8. Find the equation of the tangent line and the normal line at the point corresponding to the given value of x . 10. Find the critical points of f(x)= x^3 - 3x^2 and identify the intervals on which f is increasing and on which f is decreasing.
1) Find the linearization L(x) of f(x) at x = a.f(x) = 2x2 + 4x - 1, a = 4 2) Use implicit differentiation to find dy/dx and d2y/dx2.xy + 3 = y, at the point (4, -1) 3) Provide an appropriate response.The line that is normal to the curve x2 - xy + y2 = 25 at (5, 5) intersects the curve at what other point? 4) Find the second derivative.y = 4x2 + 10x + 2x-3 5) For the given function, find each of the following:(A) Intercepts(B) Vertex(C) Maximum or minimum(D) Rangef(x) = (x + 1)2 - 4 6) Find the slope of the line tangent to the curve y = 3x2 + 9x - 5 at the point (-2, -11). 7) Use implicit differentiation to find dy/dx.cos xy + x4 = y4 Pleas i want answer this Questions (1 -7) Analytical Geometry & Calculus

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