(1.) Find the distance between the two critical numbers of the function f(x) = x

Question

(1.) Find the distance between the two critical numbers of the function f(x) = x^3 -3x + 27. a. 1 b. 8 c. 3 d. 2 e. None of the above (2) On what interval is the function f(x) = x/x^2+1 increasing? a. [-1, 1] b. (-1, 1] c. [-1, 2] d. (-1, 2] e. None of the above (3). Find the interval on which f(x) = x + cos(x), 0_< x_< 2 is increasing. a. [ pi/3,5pi/3] b. [ 5pi/3,2pi] c. [ pi/2,3pi/2] d. [0, 2pi] e. None of the above (4) Find the absolute maximum of the function f(x) = e^-x/1+x^2 . a. 1 b. 2 c. e^-1 d. e^-1/2 e. None of the above (5) Find the minimum value of the function f(x) = x ln x?. a. -e b. -1 c. -1/e d. e^1/e e. None of the above

Explanation / Answer

1.d. 2 2.a. [-1, 1] 3.d. [0, 2pi] 4.d. e^-1/2 5.c. -1/e

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