Practice Finding Maximum And Minimum Values (5.2) - Derivatives - IB 10 Mathematics – Group 5, Calculus

Practice: Finding Maximum and Minimum Values

Lesson 5.2Derivatives

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.
What is the first step in finding maximum and minimum values of a function?
Show hintHide hint
Think about where the slope of the function is flat.
Question 2.
Define a local maximum.
Show hintHide hint
Consider how the function behaves compared to nearby points.
3Question 3.
What do critical points indicate in a function?
- They are always maximum points
- They indicate potential maxima/minima
- They are points where the function is undefined
Show hintHide hint
Consider their relationship with the derivative.
4Question 4.
True or False: A local minimum is confirmed if the second derivative is negative.
- True
- False
Show hintHide hint
Remember the signs related to the second derivative.
Question 5.
For the function $f(x) = -2x^3 + 12x^2 - 18x + 5$ , find all critical points and determine their nature.
Show hintHide hint
Start with factoring or using the quadratic formula, then check the sign of the second derivative.
Question 6.
Describe how you might use methods from calculus to optimize profit in a business scenario.
Show hintHide hint
Think about how demand can change with price adjustments.

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