2 p QUESTION 1 Let f(x) = 2x3 +5x2 - x-1. The slope of the graph of f (x) equals -1 at point O A. X = 1 O B. X = 0 OCX = 1/2 OD. X = - 1 2 poin QUESTION 2 Let f(x) = =x3 - a x+ b with a> 0. In which of the following intervals is function f(x) increasing as x increases? O A. (-a, b) O B. (- a, a ) O C. (0, 00 ) O D. ( -00, - a )2 p QUESTION 5 Consider function f(x) = a (x+1)" with a and n being constants. Suppose f"(x) = 1 for every value of x. We then know that OF a = 2 and n = 2 O B. g = 2 and n = 1 O C a = 1 and n = 2 O D. q = 1 and n = 1 2 poin QUESTION 6 Let z = h(h(x)) be a composite function, and h(x) = 1/x. Then, derivative dz/dx = O A. 1/X O B. 1 Ocx OD.OLet f(x) = =x-ax+b with a> 0. Function f(x) has a local minimum in the interval O A. (0, + 00 ) O B. (-00, 0) O c. ( -b, 0 ) O D. (-a, a) QUESTION 4 Consider function g (x, y) = pty. The partial derivative 08 (x, y) ox O A. V2 (x+ y)2 O B. xy (xty) 2 O C. V2 (x+y) OD. y (xty)2QUESTION 7 2 points Save Answe Suppose the derivative of f(x)/g(x) with respect to x equals zero, and g(x) = x in the interval (0, +0). Which of the ollowing must be true? O A f(X ) = f'( x ) O B. f' ( x ) = xf(x ) OC. A( x ) = x+ 1 O D. A( X ) = xf' ( x ) QUESTION 8 2 points Save Answer The linear approximation of function f(x) about point x=1 is given by f (x) ~ ~ (x - 1). Based on this information, function f(x) most likely takes which of the following forms? OA f (x) = x2 - 1 OB. f ( x ) = x Oc. f ( x) = Vx+1 OD . f ( x ) = V x - 1