Practice Definition (1.4.1) - Rates of Change - IB 10 Mathematics

Practise this section

10 questions

Flashcard drill
4 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
4 questions · about 3 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
Find the average rate of change of f(x) = 3x^2 - 2x from x = 1 to x = 4.
Show hintHide hint
Calculate f(4) and f(1) first.
Question 2.
What does the average rate of change represent?
Show hintHide hint
Think of it as the slope between two points.
3Question 3.
What is the formula for Average Rate of Change?
Show hintHide hint
Remember the slope concept.
4Question 4.
True or False: The Instantaneous Rate of Change is the slope of the tangent line.
- True
- False
Show hintHide hint
Think about how we derived the tangent line.
Question 5.
A cyclist travels along a path defined by the function h(t) = -4t^2 + 20t + 1. Calculate the average rate of change from t = 2 to t = 4, and then find the instantaneous rate of change at t = 3.
Show hintHide hint
Remember the formulas for AROC and IROC, and evaluate accordingly!
Question 6.
A function g(x) models the profit of a company: g(x) = 5x^2 - 10x + 15. Determine the average rate of change between x = 1 and x = 5, and explain what it indicates about the company’s profit behavior.
Show hintHide hint
Calculate the function values first!

6 more questions in this section. Enroll free to practise them all.