GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 16 Feb 2020, 22:18

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

What is the minimum value of the function

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Manager
Manager
avatar
G
Joined: 20 Aug 2017
Posts: 104
Premium Member
What is the minimum value of the function  [#permalink]

Show Tags

New post 30 Dec 2019, 05:54
5
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

47% (01:06) correct 53% (01:14) wrong based on 53 sessions

HideShow timer Statistics

Q. What is the minimum value of the function \(f(x) = 3x^2 + 6x +4\)?

A. -4
B. 1
C. 0
D. 4
E. 6
e-GMAT Representative
User avatar
V
Joined: 04 Jan 2015
Posts: 3239
Re: What is the minimum value of the function  [#permalink]

Show Tags

New post 30 Dec 2019, 10:29
1

Solution



Given
In this question, we are given that
    • A function \(f(x) = 3x^2 + 6x + 4\)

To find
We need to determine
    • The minimum value of f(x)

Approach and Working out
We can write f(x) as:
    • \(f(x) = 3x^2 + 6x + 4\)
    Or, \(f(x) = 3(x^2 + 2x + 1) + 1\)
    Or, \(f(x) = 3(x + 1)^2 + 1\)

Now, for f(x) to be minimum, \(3(x + 1)^2\) has to be minimum
    • Minimum value of \(3(x + 1)^2 = 0\)
    • Therefore, minimum value of f(x) = 0 + 1 = 1

Thus, option B is the correct answer.

Correct Answer: Option B
_________________
Intern
Intern
avatar
B
Joined: 05 Oct 2019
Posts: 10
Re: What is the minimum value of the function  [#permalink]

Show Tags

New post 30 Dec 2019, 10:50
By observation, there are only 2 possibilities to give the smallest value; (i) x = 0; (ii) x = -ve integer.

Substituting x = 0, you get 4
Substituting x = -1, you get 1
Substituting x = -2, you get 4 (you will know by now the more -ve you go for x, the bigger the value)

Hence the answer is 1
Intern
Intern
avatar
B
Joined: 26 May 2014
Posts: 1
Re: What is the minimum value of the function  [#permalink]

Show Tags

New post 16 Jan 2020, 09:31
uchihaitachi wrote:
Q. What is the minimum value of the function \(f(x) = 3x^2 + 6x +4\)?

A. -4
B. 1
C. 0
D. 4
E. 6


To get the Minimum value for the equation the Differentiation of the Equation must be equated to 0.So,
df(x) d(3x^2 +6x+4)
____ = 0 ==> _____________ = 0 ;
dx dx

6x+6 = 0
x= -1;

Putting x= -1 in equation gives the ans (3-6+4) = 1
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9417
Location: United States (CA)
Re: What is the minimum value of the function  [#permalink]

Show Tags

New post 18 Jan 2020, 12:31
uchihaitachi wrote:
Q. What is the minimum value of the function \(f(x) = 3x^2 + 6x +4\)?

A. -4
B. 1
C. 0
D. 4
E. 6


Solution:

We see that the function is a quadratic function with a positive coefficient of x^2. Thus, its graph is an up-opening parabola with its vertex as its lowest point. Therefore, the y-value of the vertex is the minimum value of the function.

The x-value of the vertex can be obtained using the formula: x = -b/(2a), where a and b are the coefficients of x^2 and x, respectively. Therefore, the x-value of the vertex is -6/(2(3)) = -1, and the y-value of the vertex, i.e., the minimum value of the function, is f(-1) = 3(-1)^2 + 6(-1) + 4 = 3 - 6 + 4 = 1.

Alternate Solution:

Alternatively, we can re-express the given quadratic function in vertex form, i.e. in the form f(x) = a(x - h)^2 + k. In this form, the coordinates of the vertex will be given by (h, k), and the minimum value of the function will be k. Setting 3x^2 + 6x + 4 equal to a(x - h)^2 + k, we obtain:

a(x - h)^2 + k = 3x^2 + 6x + 4

a(x^2 - 2xh + h^2) + k = 3x^2 + 6x + 4

ax^2 - 2ahx +ah^2 + k = 3x^2 + 6x + 4

Equating the coefficients of the quadratic terms, we get a = 3. Equating the coefficients of the linear terms and substituting a = 3, we get:

-2(3)hx = 6x

-6h = 6
h = -1

Finally, equating the constant terms, we obtain:

ah^2 + k = 4

3(-1)^2 + k = 4

3 + k = 4

k = 1

So, the vertex is (-1, 1), and the minimum value of the function is 1.

Answer: B
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
181 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

GMAT Club Bot
Re: What is the minimum value of the function   [#permalink] 18 Jan 2020, 12:31
Display posts from previous: Sort by

What is the minimum value of the function

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne