Unit 7 - Activity 1 Homework 1. Calculate the average rate of change for the function g(x)= 4x2 - 5x +1 over each interval. a. 2 S x S 2.5 2. An emergency are is shot into the air. Its height, in meters, above the ground at various times in its ight is given in the following table. mum-m S m a) Determine the average rate of change in the height of the are during each interval. i) Lostszo ii) 3.051541) b) Use your results from part a) to explain what is happening to the height of the are during each interval. 3. What is the average rate of change in the values of the function f (x) = 41: from x = 2 to x = 6'? What about from x = 2 to x = 26? What do your results indicate about x)? 1. A soccer ball is kicked into the air. The following table of values shows the height of the ball above the ground at various times during its ight. a) Estimate the instantaneous rate of change' in the height of the ball at exactlyt= 2.0 s. using the preceding and following interval method. b) Estimate the instantaneous rate of change in the height of the ball at exactly t = 2.0 s. using the centered interval method. c) Which estimation method do you prefer? Explain. 2. A crystal in the shape of a cube is growing in a laboratory. Estimate the rate at which the surface area is changing with respect to the side length when the side length of the crystal is 3 cm. 3. A spherical balloon is being inated. Estimate the rate at which its surface area is changing with respect to the radius when the radius measures 20 cm? Recall: SAsphere = 4m2