Please answer all the questions correctly with explanations.

QUESTION 1

3 2.5 f'(x ) 2 1.5 1 0.5 0+ 0.5 - 12 -1.5 -1 -0.5 0.5 1 1.5 Use the graph of f'(x) to determine the interval(s) on which f(x) is decreasing. O (-0.5, 0.5) O (-co, -0.5) and (0.5, co) O (-00, -1) O (-1, 00 )\fThe amount of medicine m in the blood during a four-hour treatment is given as mest = 3t. Determine when the amount of medicine reaches maximum. O When the time is such that e 3t = 0 O When the time is such that 3 - 3me3t = 0 O When the time is such that 3tme 3t-1 = 0 O When the time is such that me 3t = 0Which of the following could be the graph of fif f"(x) > 0 for x 0? 04 O -2 -3 5 -4 2 3 -3 -2 -4 0+ O -2 -3 2 -3 -2 -1 5 5 -4\fAt how many points on the interval [0, w] does f(x) = sinx + sin2x satisfy the Mean Value Theorem? 01 O2 03The curve x4 + xy4 = 6 has a vertical tangent when O 4xy3 = 0 O-4 - 4x3 = 0 O =0 O the curve has no vertical tangents\fIf f'(x]- $1.4 + $5 +212 + 1 determine the xvalue{s} where fix} changes from concave up to concave dawn. Oxz Ox=1 Ox=4 10 2 04 -2 -4 -6 -105 -4 -3 -2 2 3 Graph of g Use the graph of g' to justify if g has a relative minimum at x = 2. O No, because g' is changing from negative to positive at x = 2 O No, because g' is changing from positive to negative at x = 2 O Yes, because g' is changing from positive to negative at x = 2 O Yes, because g' is changing from negative to positive at x = 2The second derivative of the function g is given by g"(x) = 2 Given x = 0.4 is a critical point of g, use the Second Derivative Test to determine relative extrema for g. O g has a point of inflection at x = 0.4. O g has neither a relative minimum nor relative maximum at x = 0.4. O g has a relative maximum at x = 0.4. O g has a relative minimum at x = 0.4