Calculus Questions

3. [-/12.5 Points] DETAILS SCALCET8 4.3.503.XP.MI. Consider the equation below. F(x) = 2x3+ 3x - 180x (a) Find the interval on which f is increasing. (Enter your answer in interval notation.) Find the interval on which f is decreasing. (Enter your answer in interval notation.) (b) Find the local minimum and maximum values of f. local minimum local maximum (c) Find the inflection point. (x , y) = ( Find the interval on which fis concave up. (Enter your answer in interval notation.) Find the interval on which fis concave down. (Enter your answer in interval notation.) Need Help? Watch It Master It4. [-/12.5 Points] DETAILS SCALCET8 4.3.068. Let ((t) be the temperature at time & where you live and suppose that at time t = 3 you feel uncomfortably hot. What happens to the temperature in each case? (a) f '(3) = 1, f "(3) = 3 O The temperature is increasing, and the rate of increase is increasing. O The temperature is increasing, but the rate of increase is decreasing. The temperature is decreasing, but the rate of change is increasing (becoming less negative). O The temperature is decreasing, and the rate of change is decreasing (becoming more negative). (b) f '(3) = 1, f "(3) = -3 O The temperature is increasing, and the rate of increase is increasing. O The temperature is increasing, but the rate of increase is decreasing. O The temperature is decreasing, but the rate of change is increasing (becoming less negative). O The temperature is decreasing, and the rate of change is decreasing (becoming more negative). (c) f '(3) = -1, f "(3) = 3 O The temperature is increasing, and the rate of increase is increasing. O The temperature is increasing, but the rate of increase is decreasing. The temperature is decreasing, but the rate of change is increasing (becoming less negative). The temperature is decreasing, and the rate of change is decreasing (becoming more negative). (d) f '(3) = -1, f "(3) = -3 O The temperature is increasing, and the rate of increase is increasing. O The temperature is increasing, but the rate of increase is decreasing. O The temperature is decreasing, but the rate of change is increasing (becoming less negative). O The temperature is decreasing, and the rate of change is decreasing (becoming more negative)