106. Absolute maximum at x = 4, absolute minimum at x = -1, local maximum at x = -2, and a critical point that is not maximum or minimum at x = 2
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Draw a graph over the interval [-4, 4], with the following properties.
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- How are the absolute maximum and minimum similar to and different from the local extrema?Discuss the extreme-value behavior of the function ƒ(x) = x sin (1/x), x ≠ 0. How many critical points does this function have? Where are they located on the x-axis? Does ƒ have an absolute minimum? An absolute maximum?Determine where the absolute extrema of f(x) = -3x^2 + 10x on the interval [1, 3] occur. Absolute maximum occurs at x = Absolute minimum occurs at x =
- Consider the function ƒ(x) = x3. Where is the critical pointof ƒ? Does ƒ have a local maximum or minimum at the critical point?(d) Find all x- values in the interval -5 < x < 5 at which g has a critical point. Classify each critical point as the location of a local minimum, a local maximum, or neither. Justify your answers.Graph afunction on the interval [−2, 5] having the givencharacteristics.Relative minimum at x = −1Critical number (but no extremum) at x = 0Absolute maximum at x = 2Absolute minimum at x = 5
- What values of a and b make ƒ(x) = x3 + ax2 + bx have a. a local maximum at x = -1 and a local minimum at x = 3? b. a local minimum at x = 4 and a point of inflection at x = 1?Shown is the graph of the derivative f'(x) of the function f(x). (a) Identify the critical numbers of f(x). (b) For each critical value, determine whether it is a local maximum, local minimum, or neither. (c) Is f''(−2) positive or negative? What can you say about the concavity of the original function f(x) nearby x = −2?2. Give an example showing that, even if f0(c) = 0, it could happen that f(x) does not have a localmaximum or minimum at x = c. How is this consistent with Fermat’s Theorem in the book?
- Find the absolute extrema of the function h(x) = ex2 − 4 on [−2, 2] Absolute maximum value: at x = ± Absolute minimum value: at x =Find the points at which y=f(x)=4x−ln(2x)y=f(x)=4x−ln(2x) has a global maximum, a global minimum, and a local, non-global maximum on the interval .1≤x≤3 Round your answers to two decimal places.a) On the number line, mark the critical value(s) of f(x) and the sign of the first derivative between them as obtained from the graph. b) Where is f(x) increasing on it's domain? c) Where is f(x) decresing on it's domain? e) At what x-value(s) would f(x) have a relative maximum? d) At what x-value(s) would f(x) have a relative minimum?