determine the locations of internal or external

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Calculus exam

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1. Given f(x) = sin(3x+1), h(x) = (x and g(x) = cos(x²) a. Find (f(x) +h(x) + g(x)) b. Find (x2 f(x)) C. Find ((x - x - 3)g(x)) d. Find (x? g(x)) dg(x) e. Find dx d dx (x) = 2. Given f(x) = 2x2 + 3x – 2,g(x) = sin(x), h(x) = cos x, k(x) = a. Find á f(g(x))for x = 1 b. Find 9(f(x))for x = -1 c. Find f((k(x)) for x = 2 d. Find h((k(x)) for = 1 e. Find g(h(x)) for x = -1 f. Find (f(x)) for x = 1 3. For the following functions, determine the locations and of relative and absolute extrema, either minimum or maximum, and their values. a. f(x) = (x - 2)2(x + 3) with domain (-23] b. h(x) = sin ( - 1) with domain (0,4] x- c. k(x) with domain (-1,1] d. g(x) = with domain (1,5) = 2x2+1 x-1 x2+1 5 4 3 2 1 3 x 2 4 -1 -2. -3 -5 4. Concerning the graph a. Locate the coordinates (x, y) for all the relative maximum b. Locate the coordinates (x, y) for all the relative minimum c. Locate the coordinates (x, y) for the absolute maximum d. Locate the coordinates (x, y) for the absolute minimum e. Compare the following values to 0, i.e., = 0, 0 or DNE ('does not exist) 1. f'(-3) 2. f'(-3.5) 3. f'(-2) 4. f'(-1) 5. f'(1) 6. f'(2) 7. f'(3) 8. f'(4) 9. f"(-3) 10.f"(4) 11.f"(3) 12.f"(-2) 13.f"(1) 2x+3 - dx 5. Indefinite integral a. SG (x2+38-10) b. Sr 5r2 + 2 dr c. S V1 + Vedx d. S(2x - 9 cos x) dx e. S(sin x – 2 sec? x)dx 6. Definite Integrals: a. 123 (024792 dx b. 2x (x2+1) x2 +3 VX2-4 dx dx d. Si cos de 2V1-sino 144 25 7. Given an elliptical boundary of an area with the equation += 1, a farmer wants to enclose a rectangular pen such that it maximizes the area of the pen for grazing. What are the dimensions of the pen?
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I was struggling with this subject, and this helped me a ton!

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