2- 1. 2 3 -1- -2- Graph of f' Let f be the function defined by f (x) E -E. The graph of f', the derivative of f, is shown above. On which of the following intervals is the graph of f concave up? A x < -1 and 0 < x < 2 (B) -1 < x <0 and a > 2 and æ > + 3 2/10 2/10
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- The function f(x) is continuous and differentiable on the interval [−2,6]. It is known that f(−2)=4 and the derivative on the interval satisfies the condition f′(x)≤3 for all x∈(−2,6). Determine an upper bound of the function at the right endpoint x=6.The rule of the derivative of a function f is given. Find the location of all local extrema.f'(x) = (x + 5)(x + 2)(x - 4)f and g are differentiable functions that sum is a constant ( f (x) + g(x) = k for all x) what can be concluded about their graph and or derivatives?
- Consider the function on the interval (0, 2π). (a) Find the open intervals on which the function is increasing or decreasing. (b) Apply the First Derivative Test to identifyall relative extrema. (c) Use a graphing utility to confirm your results.Limit represents the derivative if sime function f at some number a. State such an f and a in each case1)Describe the purpose of finding the first and second derivatives to sketch a graph of functions. 2)Find all relative extrema using the second derivative test. a. f(x) = x^2(6 − x)^3b. g(x) = x^3 −5x2 +7x
- draw a graph to match the description given. f(x) has a negative derivative over (-infinity, 2) and (2,7), a positive derivative over (7, infinity) and a derivative equalt to 0 at x=2.Consider the function on the interval (0, 2π). (a) Find the open intervals on which the function is increasing or decreasing. (b) Apply the First Derivative Test to identify all relative extrema. (c) Use a graphing utility to confirm your results. f(x) = x − 2 sin x1) Describe the purpose of finding the first and second derivatives to sketch a graph of functions. 2) Find all relative extrema using the second derivative test.a. f(x) = x^2(6 − x)^3b. g(x) = x^3 −5x^2 +7x
- Let h be the function h(x) = 2x2. The value of x decreases as x changes from −2 to −1. TRUE OR FALSE As x changes from −2 to −1, h(x) changes from .... to .... As x changes from −1 to 1, h(x) changes from .... to .... 4. The average rate of change of h on the interval from −1 to 1 is greater than the average rate of change of h on the interval from −2 to −1. TRUE OR FALSE? Justify by calculating both average rates of change. Show all work. 5. Mark the correct answer. h(x) is concave up. concave down. neither. both PLEASE HELP ME WITH THEM ALL. THANK YOUUConsider the function on the interval (0, 2π ). (a) Find the open intervals on which the function is increasing or decreasing. (b) Apply the First Derivative Test to identify all relative extrema. (c) Use a graphing utility to confirm your results f(x) = sin x − √3 cos xConsider a function f(x)f(x) whose derivative is given by f′(x)=((x−1)(x+2))/x(1+x2). Find the following. Number of intervals on which ff is decreasing Number of local maxima Number of intervals on which ff is increasing Number of local minima