Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
5.6k views
in Derivatives by (28.3k points)
closed by

The minimum value of f(x) = x4 – x2 – 2x + 6 is :

A. 6 

B. 4 

C. 8 

D. none of these

1 Answer

+1 vote
by (29.4k points)
selected by
 
Best answer

Option : (B)

f(x) = x4 - x2 - 2x+ 6 

f’(x) = 4x3 - 2x - 2 

so here put f’(x) = 0 

4x3 - 2x - 2 = 0 

2(x - 1)(2x+ 2x + 1) = 0 

x = 1 and other roots are complex. 

so we will consider x = 1 

Hence by second derivative test  

f’’(x)>0 so it’s a point of minimum. 

f”(x) = 12x- 1 

f” (1) = 12(1) - 2 

= 10 > 0 

At x =1 minimum 

So, 

f(1) = 1 - 1 - 2(1) + 6 

= 4

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...