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3. Let h be a function whose first derivative is h/(x) = S:* 3(In( + 3))? dt. For 6 < x < 12, which of the following is true? Oh is increasing and the graph of his concave down. Oh is increasing and the graph of h is concave up. Oh is decreasing and the graph of h is concave down. 0 h is decreasing and the graph of h is concave up. Oh...
2. Let f(x) = 8 + 3x4 -1 5x<1, f(x+2) = f(x). Which best describes the Fourier series of f: (a) It is a Fourier cosine series. (b) It is a Fourier sine series. (c) It is a general Fourier series with sine and cosine terms.
Match each function with its graph Function Graph Color a. red If'(x) f''(x) b. green c. blue 2 -54 -3 -2 -1 1 2 3 4 5 1 -2 a The function graphed above is decreasing on the interval << The inflection point is at x =
Find the required Fourier Series for the given function f(x).
Sketch the graph of f(x) for three periods. Write out the first
five nonzero terms of the Fourier Series.
cosine series, period 4 f(0) = 3 if 0<x<1, if 1<x<2 1,
Sketch the graph of a single function that has all of the properties listed. (a) Continuous and differentiable everywhere except at x = 2, where it has a vertical asymptote (b) Increasing everywhere it is defined (c) Concave upward on (-0,2) and (446) (d) Concave downward on (2,4) and (6,00) Choose the correct graph below. OA ов. O c. OD a 10 10 10 10 10 10 10 - 10
Consider the following function. (If an answer does not exist, enter UN 36 f(x) = x + х (a) Find the intervals where the function is increasing and where it is decreasing. (Enter your answer using interval notation.) increasing decreasing (b) Find the relative extrema of F. relative maximum (X,Y) - relative minimum (X,Y) - (c) Find the intervals where the graph of fis concave upward and where it is concave downward. (Enter your answer using interval notation.) concave upward...
Summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of f(x) = + 2x-15 ² Summarize the pertinent information obtained by analyzing f(x). O A. f(x) is decreasing on (-00, 0) and (0, 15) and increasing on (15,..). O B. f(x) is increasing on (-00, 0) and (15, 0o) and decreasing on (0.15). OC. f) is decreasing on (-0, 0) and (15,00) and increasing on (0, 15). OD. f(x) is increasing on (-0,0) and (0,...
Sketch a graph of the piecewise defined function. sz if x <3 f(x) = x 1 if x 2 3
EXAMPLE 3 Sketch the graph of x) = 5xe". (A) The domain of f is R. (B) The x- and y-intercepts are both (C) Symmetry: None. (D) Because both 5x and ex become large as x →oo, we have limx→”5xex=00, As x →-oo, however, ex→ and so we have an indeterminate product that requires the use of l'Hospital's Rule: 5xlim Video Example Thus the x-axis is a horizontal asymptote (E) f(x) = 5xex + 5e" = Since ex is always...
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Let f(x) = 23 + 9x² – 812 +21. (a) Use derivative rules to find f'(x) = 3x2 +18% -81 (b) Use derivative or the derivative rules to find f''(x) = 60 + 18 (c) On what interval is f increasing (include the endpoints in the interval)? interval of increasing = (-0,-9] U [3,00) (d) On what interval is f decreasing (include the endpoints in the interval)? interval of decreasing = [-9,3] (e) On what interval is f...