Loading the lesson
Loading the lesson
Search AllRounder.ai
Search the courses, subjects, tracks, games and features, or jump straight to a page.
Search the courses, subjects, tracks, games and features, or jump straight to a page.
5 cards from this section. Quick, good the night before a test.
Find the local maximum or minimum of f(x) = x² − 6x + 5 and its value.
Set the derivative equal to zero, then check the sign of the second derivative.
Find the local maximum value of f(x) = −x² + 4x + 1.
A negative second derivative means a maximum.
At x = c, f′(c) = 0 and f′ changes from negative to positive. What does f have at c?
Think of going downhill and then uphill.
At x = c, f′(c) = 0 and f″(c) = 0. What can you conclude?
Remember the examples x⁴ and x³.
An open box with a square base must hold 32 cm³. Find the dimensions that use the least material.
Use the volume to write the height in terms of x, then minimise the surface area.
Show that, of all rectangles that can be inscribed in a circle of radius r, the square has the largest area.
The diagonal of an inscribed rectangle is a diameter of the circle, and maximising A² is easier than maximising A.
6 more questions in this section. Enroll free to practise them all.
Enroll free