For a function defined on an an interval , as shown in the graph below, which of the statements is correct?

I. The absolute maximum value of the function is

II. Local minima is

III. Local maxima occurs at

IV. The absolute minima occurs at

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Calculus 1

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Find extreme values and critical points

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Zhen ZhuLv5

7 Jan 2021

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Sketch the curve having two local maxima and local minima in the interval for an even function. One of the maxima occurs at . Maximum value is , local minima occurs at , and minimum is . Also, there exists a global maxima at .

6. (14 pts) EXPLANATION IS NOT REQUIRED, AND NO PARTIAL CREDIT WILL BE GIVEN. The graph of f'(derivative of f) on the interval [-6, 7] is shown in the figure. y f(x) y = f'(x) -6 -5 -4 -3 2 L - 2 3 4 5 7 Use the given graph of f' to answer the following questions about f: (a) (2 pts) on what interval (or intervals) is f decreasing? (b) (3 pts) Find the critical points of f. (c) (2 pts) which critical points (or point) correspond to local maxima ? (d) (2 pts) which critical points (or point) correspond to neither local maxima nor local minima ? (e) (2 pts) on what interval (or intervals) is f concave up? (f) (3 pts) At what point (or points) does f have an inflection point ?

4. (30 pts) EXPLANATION IS NOT REQUIRED, AND NO PARTIAL CREDIT WILL BE GIVEN. (I) The entire) graph of a function f is shown in the figure below. (a) Find the x-coordinates of all critical points of f (or write NONE). ANSWER : critical point (s) at x = (b) Find the x-coordinates of all local minima of f (or write NONE). ANSWER : local min (s) at x = (c) Find all values of x at which fattains its global minimum (or write NONE ANSWER : global min (s) at x = (d) Find the interval (or intervals) on which the derivative of fis increasing. ANSWER : derivative off is increasing on (II) The figure below shows the graphs of f, f', and f". Which curve is which? Fill in the blanks: A = -; B= 2; CD- 4. EXPLANATION IS NOT REQUIRED, AND NO PARTIAL CREDIT WILL BE GIVEN. (III) A function f' (derivative of f) is given f'(x) = (x - 2) e*. The following questions are about the function f. (a) Find all critical points of f (or write NONE). ANSWER : critical point (s) at x = (b) on what interval (or intervals) is f increasing ? ANSWER : f is increasing on (c) Find the point or points where f has a local maximum (or write NONE). ANSWER : local max at x = (d) Find the point or points where f has a local minimum. ANSWER: local min (s) at x = (e) Find f "(x), the second derivative of f. ANSWER : f''(x) = (f) Identify any inflection pionts. ANSWER : inflection point (s) at x = (g) Determine the intervals on which the function is concave up or concave down. ANSWER: fis CONCAVE UP on fis CONCAVE DOWN on

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For a function defined on an an interval , as shown in the graph below, which of the statements is correct? I. The absolute maximum value of the function is II. Local minima is III. Local maxima occurs at IV. The absolute minima occurs at

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For a function defined on an an interval , as shown in the graph below, which of the statements is correct?

I. The absolute maximum value of the function is

II. Local minima is

III. Local maxima occurs at

IV. The absolute minima occurs at