POWER f"(x)>@ concave up Nan Question 1. Indicate if each statement is true or false. Justify your claim. (a) A function is increasing if the slope of the tangent lines are negative. (b) The First Derivative Tests tells where the function is increasing or decreasing. T (c) If f'(3) = 0, f'(1) = -6, and f'(5) = -9, then there is a relative minimum when x = 3. (d) Critical numbers only occur when the first derivative is 0. (e) All critical numbers are minimums or maximums. (f) A function is decreasing when the second derivative is less than 0. (g) The Second Derivative Test tells where there are inflection points. (h) The point of diminishing returns meas a local max or min. (i) The absolute maximum of a functions always occurs where the derivative has a critical number.Question 2. For each function, find (a) the critical numbers (b) open intervals where the function is increasing. and (c) open intervals where the function is decreasing. (a) f(x) = 4x3 - 15x2 + 72x +5 f ( x )= 12x - 30* + 72 b - - 30 * V(:30) - 4 (12 ) ( 72 ) 2 ( 12 ) (b) y = 1 - 4In(3x - 9) (c) g(x) = 122-2