5. The function f(x) has a derivative g(x), shown on the graph below. (2, 1) (0, 1) 1- 1 (4,-1) (-3,-2)- Graph of g Find the x-coordinate of each critical point of f(x) on the interval -3
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- Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it continues on its course indefinitely. Let D(t) denote its distance from Earth after t years of travel. Do you expect that D has a limiting value?Consider a function y =f(t) with domain (0. 1, 4. 2).Use the graph of the derivative function, y=f'(t) ,given below to write down the t -value of the local maximum of f. If the function has no local maximum, explain why notThe 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
- Find the vertical and horizontal asymptotes of f(x), find the first and second derivatives and draw the graph of the following function. Be precise on the values in the range -4 to 4 and on the critical values of the derivatives: f(x)= ( (x^3)+8) / ((x^3-8)) How would the graph change if it were f(x) = ( (x^3)+8) / ((x^3-8)) +13. 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.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?
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- 1. What is the critical point of the function f (x) = cos x? 2. What is the maximum point of the function f (x) = x² - x on the interval [-2,2]? 3. Given the interval [ -2,2] for the function f (x) = -8x² + 2x⁴ ; at which value/s of x will the maximum point occur?a. Locate the critical points of ƒ.b. Use the First Derivative Test to locate the local maximum and minimum values.c. Identify the absolute maximum and minimum values of the functionon the given interval (when they exist). ƒ(x) = √x ln x on (0, ∞)