f(x) = x^3 - 3x^2 - 9x + 4. Match each item in List I with its value in List II. | List I | List II | |---|---| | A. Point of local maximum | I. 9 | | B. Point of local minimum | II. -1 | | C. Local maximum value | III. -23 | | D. Local minimum value | IV. 3 |

f(x) = x^3 - 3x^2 - 9x + 4. — CUET Maths practice

f(x) = x^3 - 3x^2 - 9x + 4.

Question 34

MediumOriginal question

$f(x) = x^3 - 3x^2 - 9x + 4$ . Match each item in List I with its value in List II.

List I	List II
A. Point of local maximum	I. $9$
B. Point of local minimum	II. $-1$
C. Local maximum value	III. $-23$
D. Local minimum value	IV. $3$

A-II, B-IV, C-I, D-IIICorrect answerYour answerA-IV, B-II, C-I, D-IIICorrect answerYour answerA-II, B-IV, C-III, D-ICorrect answerYour answerA-IV, B-II, C-III, D-ICorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

$f'(x) = 3(x - 3)(x + 1)$ and $f''(x) = 6x - 6$ : $f''(-1) = -12 < 0$ (maximum) and $f''(3) = 12 > 0$ (minimum).
$f(-1) = -1 - 3 + 9 + 4 = 9$ and $f(3) = 27 - 27 - 27 + 4 = -23$ .

Concept: Points and values of local extrema
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsThe second 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.

f(x) = x^3 - 3x^2 - 9x + 4.

Question 34

Explanation