Question 1 Part A

What is the derivative of y = (cos 14x2)3? -24x V1-16x" Oy's -16x cos (4x2) V1-16x" Oy's -3(cos 14x2)2 V1-16x Oy= -24 x(COS 14x2)2 V1- 16xWhich of the following functions is guaranteed by the Extreme Value Theorem to have an absolute minimum on the interval [-7, 7]? Offx) = In(5x) O r(x) = V5x Of(x) = -cos(5x)Let h be a continuous function for x 3 0, with its first derivative given by (x)- 4." -4x + _, Determine the interval(s) where the graph of his concave up. O (0. 0.707) O (0.707, 60) O (0.529, 00) O (0. 0.529)Question 4(Multiple Choice Worth 10 points) (03.07 MC) Let f be a function given by /(x) = - x' + x + 2 What is the instantaneous rate of change of f' at x = -1? 06 04 0-4 176 105A forest fire is spreading such that the area of the burning region in square miles after d days can be modeled by F(d) . 3+d At what rate is the area of the buming region changing after 2 days? O-1.995 mi /day O 0.398 mi-/day O 1.596 mi-/day O 7 979 mi-/day0 -1 2 2 0 2 10 12 14 A linear approximation at x = 2 will result in O an underestimate because the tangent line falls below the curve O an underestimate because the tangent line falls above the curve Ofan overestimate because the tangent line falls below the curve O an overestimate because the tangent line falls above the curve\fA particle moves along the x-axis such that its position at time f is given by x(1) = -4 + 3: for f 2 0. At what time is the particle speeding up? Of= 0.25 Of=0.572 Of= 0.75Selected values of f' and f", where fis a twice-differentiable function, are shown in the table. X -1 0 0.375 0.75 1 1.125 2 f" (x ) -17 0 -0.844 -1.688 -1 0 28 f" (x) 42 10 -3.375 0 6 10.125 60 Which of the following statements is true? Ofhas a local minimum at x = 0 Of has a local maximum at x = 0 Ofhas a local minimum at x = 1.125 Of has a local maximum at x = 1.125