1. For f(x)=x2, determine the average rate of change of f(x) with respect to x over each interval. (9 marks) a. 1≤x≤1.5
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- 1 For F X X2 Determine The Average Rate Of Change Of F X With Respect To X Over Each Interval 9 Marks A 1 X 1 5 1 (159.98 KiB) Viewed 36 times
1. For f(x)=x2, determine the average rate of change of f(x) with respect to x over each interval. (9 marks) a. 1≤x≤1.5 b. 1≤x≤1.1 c. 1≤x≤1.01 2. Determine the average rate of change of g(x)=4x3−5x+1 over each interval. ( 9 marks) a. 2≤x≤2.1 b. 2≤x≤2.01 c. 2≤x≤2.001 3. Copy and complete the table. Then estimate the instantaneous rate of change of f(x)=5x2+3 at point (2,23).(12 marks) 4. Estimate the instantaneous rate of change of each function at the given point. (6 marks) a. f(x)=x3+x2 at (2,12) b. f(x)=−x4+1 at (3,−80) 5. A pebble falls from the top of a cliff that is 180 m high. The pebble's height above the ground is modelled by h(t)=−5t2−5t+180 where h is the height in metres at t seconds since the pebble started to fall. (10 marks) a. Find the average rate of change between 1 s and 4 s. b. Find h(3) c. Find the instantaneous rate of change of height at 3 s. d. Explain the meaning of each value calculated in parts a,b and c. Copyright @ 2011, Durham Continuing Education Page 36 of 70 MCV4U - Calculus and Vectors Unit 1 - Lesson 3 6. The population of a town is modelled by P(t)=6t2+110t+3000, where P is the population and t is the number of years since 1990. (9 marks) a. Find the average rate of change in population between 1995 and 2005. b. Find P(15) c. Estimate the rate at which the population is changing in 2005 .