\f3. Find the average rate of change of d(t) between the values (a) t = 1 sec. and t = 3 sec., between (b) t = 2 sec. and t = 3 sec., between (c) t = 2.5 sec. and t = 3 sec., and between (d) t = 2.9 sec. and t = 3 sec.5.7. A projectile is shot upward with an initial velocity of 96 ft/sec. The equation for the height of the projectile after t seconds is h(t)= -1612 + 96t + 256. a. The velocity function (or rate of change of the height) is the derivative of h(t). Find this derivative function.2. If a continuous function attains a maximum or minimum value on a given interval, what conclusion, if any, can you make about the value of the derivative at the maximum or minimum? Justify your answer.The Connection to Limits 6. Notice that your answers for each interval supplied above seem to be approach- ing what is known as a limit or limiting value. Can you estimate this value?Question 5 12.5 pts In Exploration 5.3.2 Question 3. you found multiple average rates of change 1with different intervals. Then, in question 6. you estimated the limiting value that the average rates of change were approaching. What is that value? Question 6 12.5 pts In Exploration 5.3.3, the velocity vs. time graphs were given and you were asked to create a graph of the corresponding acceleration-time. Which of the following is the correct acceleration vs. time graph for Question 5? C) WWW Question 7 12.5 pts In Exploration 5.4.1 Question Hal, you 1were asked for the velocity {rate of change of the height}. Select the correct VEIOCitY function. 0 H13}: 1t + Q 0 Hit) = 42: + 9'5 0 hr {1} = 32t + 352 0 H {t} 2 _at3 +43t + 25m. 0 if {t} = 32t Question 3 12.5 pts In Exploration 5.4.2 Question 2. what conclusion can vou make about the value of the derivative at the maximum or minimum for a continuous function? C} The value can not be determined without more information. C} The value of the derivative represents the slope of the tangent line which will be horizontal at a relative maximum or minimum. Therefore the value of the derivative is zero. C} The value of the derivative will equal the v-value at that location. 0 The value of the derivative is , which is derived from the quadratic equation and is part of the quadratic formula