Maths 4.3Lesson outlineLesson 3 of 9 in Module 4
Maxima, Minima and Setting the Derivative to Zero
Find where a function is lowest or highest, and know when that cannot be done by solving an equation.
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In this lesson10 parts
- 01Where the slope is zero
- 02Solving f′(x) = 0
- 03Local and global
- 04No minimum at all
- 05No formula for the answer
- 06Checkpoint: minima so far
- 07The best single prediction for six prices
- 08Absolute error and the median
- 09Minima in Python
- 10Recap, challenge, and next: the gradient
Key terms
The words this lesson introduces, each in one line. The module’s glossary collects them all.
- stationary point
- a point where the derivative is zero |
x² − 3x + 2at1.5 - minimum
- the derivative changes from negative to positive |
f′(1) = −1,f′(2) = 1 - maximum
- the derivative changes from positive to negative |
x⁴ − 4x² + xat0.126 - local minimum
- lower than every nearby point |
1.347, value−2.6186 - global minimum
- lower than every point |
−1.473, value−5.4442 - bisection
- halve an interval that contains a zero, keeping the half where the sign changes |
2x + eˣ = 0on[−1, 0] - iterative method
- a method that improves an answer step by step | bisection, gradient descent
- median
- the middle value; it minimises the sum of absolute errors |
13.2for the six hero prices
Quiz
Your first pick on each question is the one that counts, and a right one earns a coin. Getting one wrong here is how the lesson sticks.