EduFarming
Your list · 0हिं

Type at least two letters. Press Esc to close.

↑↓ navigate↵ openTAB cycle filter

Maxima & Minima · Question 24 of 80

Question 24

MediumOriginal question

What are the critical points of f(x)=x4−4x3f(x) = x^{4} - 4 x^{3}?

Options for question 24

Show the answer and explanation
CorrectNot quiteAnswer B

Correct answer: B

Explanation

  1. Critical points are where f′(x)=0f'(x) = 0: f′(x)=4x2(x−3)f'(x) = 4 x^{2} \left(x - 3\right).

  2. So x=0,3x = 0, 3.

Worth noting

A repeated factor such as x2x^{2} still gives a critical point, even though f′f' does not change sign there.

Concept
Finding critical points
Typical time
90 s
Your time
—
The rule this testsLocal extrema and the first derivative test
Practise this chapter →

Ten questions from Maxima & Minima, at your own pace.

Practise this chapter →

Ten questions from Maxima & Minima, at your own pace.