Use the graph of the function f(x) to locate the local extrema and identify the
ID: 2892868 • Letter: U
Question
Use the graph of the function f(x) to locate the local extrema and identify the intervals where the function is concave up and concave down. A) Local maximum at x = 3: local minimum at x = -3: concave down on (0, -3) and (3, infinity): B) Local minimum at x = 3: local maximum at x = -3: concave up on (0, -3) and (3, infinity): concave down on (-3, 3) c) Local minimum at x = 3: local maximum at x = -3: concave up on (0, infinity): concave down on(-infinity, 0) D) Local minimum at x = 3, local maximum at x = -3: concave down on (0, infinity): concave up on (-infinity, 0) Provide an appropriate response. Find the absolute maximum and minimum values of f(x) = 9x^3 - 54x^2 + 81x + 13 on the interval [-6, 2]. A) max f(x) = f(1)) = 4362 min f(x) = f(-6) = 49 B) max f(x) = f(1) = 4361 min f(x) = f(-6) = -49 C) max f(x) = f(1) = 49 min f(x) = f(-6) = -4361 D) max f(x) = f(-6) = -4361 min f(x) = f(1) = 49 Find the absolute maximum and absolute minimum values of the function f(x) = x^4 - 6x^2 on the interval [0, 3]. A) Absolute maximum: f(3) = -27: absolute minimum: f(Squareroot 3) = -9 B) Absolute maximum: f(0) = 0: absolute minimum: f(2) = -8 C) Absolute maximum: f(3) = 27: absolute minimum: f(Squareroot 3) = -9 D) This function has no absolute maximum or minimum on the given interval. Find the absolute maximum and minimum values of the function f(x) = 4x/x^2 + 1 on the interval A) Absolute maximum is 0 at x = 0. Absolute minimum is 2 at x = -1. B) Absolute minimum is at x = -1. Absolute maximum is -2 at x = 0. C) Absolute maximum is 0 at x = 0. Absolute minimum is -2 at x = -1. D) Absolute minimum is 0 at x = 0. Absolute maximum is -2 at x = -1.Explanation / Answer
13) From graph we can clearly see that option C is the right answer
because in the region (-infinity, 0) curve is downward parabola so concave down and hence making a slope 0 at x = -3 hence a local maximum.Similarly in the region (0,infinity) the curve is upward parabola so concave up and hence making a slope 0 at x =3 hence a local minimum.