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QUESTION 1 Let f(x) =(x2 + 1)"(2x - 1) is a polynomial function of fifth degree. Its second derivative is f"(x) = 4(x2 + 1)(2x - 1) + 8x2(2x - 1) + 16x(x2 + 1) and third derivative is f"(x) =24x(2x - 1) + 24(x2 + 1)+ 48x2. True o False QUESTION 2 Given the equation x3 + 3xy + 3 = 4. We find by implicit differentiation and is to be y = - _ x2 + v x+ 2 ' o True o False QUESTION 3 Let f(x) = vx + 1 is a principal square root function. Therefore, the differential of f(x) is found to be dy = 2vx dx. o True o False QUESTION 4 Let y = f(x) define a differentiable function of x. Then, the differential dx of the independent variable x is dx = Ax and the differential dy of the dependent variable y is dy = f (x)Ax =f (x)dx. o True False QUESTION 5 Let f(x) = is a rational function. Therefore, the differential of f(x) is found to be dy = =" + 2x+ 1 x2 + 1 ( x 2 + 1 ) 2 o True o False QUESTION 6 Let f(x)= =x3 - x2 - 12x +3 is a polynomial function of third degree. Its first derivative is f (x) =2(x -3)(x + 2) and it is continuous everywhere. The zeros of f (x) are x=-2 and x=3. Evaluating the first derivative's sign (that shows either function is increasing or decreasing) on the found intervals for x: to the left of -2, between -2 and 3, and to the right of 3; we find that f(x) is increasing on the interval (-2,3) and decreasing on the intervals (-oo, - 2) and (3, + 0o). True o False