(8 points) Find all critical points and classify them via the second derivative test. (a) f(x,y)...
(a) Use the second derivative test to find and classify the critical points for the following function. Don’t forget to find the Y-coordinate of the local extremas. f(x) = e x−4 (x 2 − 10x + 17) (b) Find the area enclosed between the curves √ x and x 3 . (You need to sketch the graphs) f(x) = e*-4.x? 10x + 17). vr and 2.3.
Find the critical point of the function. Then use the second derivative test to classify the nature of this point, if possible. (If an answer does not exist, enter DNE.) f(x, y) = x2 − 4xy + 2y2 + 4x + 8y + 8 critical point (x, y)= classification ---Select--- :relative maximum, relative minimum ,saddle point, inconclusive ,no critical points Finally, determine the relative extrema of the function. (If an answer does not exist, enter DNE.) relative minimum value= relative...
(a) A function / has first derivative f'(z) = and second derivative 3) f"(x) It is also known that the function f has r-intercept at (-3,0), and a y-intercept at (0,0) (i) Find all critical points, and use them to identify the intervals over which you will examine the behaviour of the first derivative ii) Use the f'(), and the First Derivative Test to classify each critical point. (ii) Use the second derivative to examine the concavity around critical points...
(1 point) Find the critical points of f(x) and use the Second Derivative Test of possible) to determine whether each corresponds to a local minimum or maximum. Let f(x) = x exp(-x) e lest ? Critical Point 1 - Critical Point 2 - is what by the Second Derivative Test? is what by the Second Derivative Test?
2. Find and classify all critical points for f(x,y) = -22 + y? (x - 8)
Find the critical points of and use the second derivative test to classify these points as saddle, local minimum and local maximum points.
(a) Find and classify all of the critical points of the function X f(x, y, z) = (x2 +42 + x2)3/2 on the unit sphere. (b) Find and classify all of the critical points of the function f(x, y, z) = x sin(x2 + y2 +22) on the sphere of radius
Find all relative extrema and classify them. Use the Second Derivatives Test. f(x, y) = x² + 2xy – 2y? – 10x
4. (a) A function f has first derivative f'(x) and second derivative 2 f" (x) It is also known that the function f has r-intercept at (-3,0), and a y-intercept at (0,0) (i) Find all critical points, and use them to identify the intervals over which you will examine the behaviour of the first derivative. 3 marks] (ii) Use the f(x), and the First Derivative Test to classify each critical point.[3 marks] (iii) Use the second derivative to examine the...
4. (a) A function f has first derivative f' (x) - and second derivative f"(x) It is also known that the function f has r-intercept at (-3,0), and a y-intercept at (0,0) (i) Find all critical points, and use them to identify the intervals over which you will examine the behaviour of the first derivative. 3 marks] (ii) Use the f'(x), and the First Derivative Test to classify each critical point. 3 marks (iii) Use the second derivative to examine...