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14 Jul 2024, 10:20
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Difficulty:
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Question Stats:
64% (01:53) correct
36%
(02:01)
wrong
based on 187
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What is the minimum value of the function f(x) = x^2 − 9x − 11 for all real values of x?
A. -125/4
B. -145/4
C. -37/4
D. 37/4
E. -81/4
A. -125/4
B. -145/4
C. -37/4
D. 37/4
E. -81/4
15 Jul 2024, 08:44
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step 1 - find f'(x)
f'(x)=2x-9
step 2 - put f'(x)=0
2x-9=0
x=9/2 [max/min pt]
step 3 - to check max or min, find f''(x)
- if f''(x)>0 [pt of min]
- if f''(x)<0 [pt of max]
In this case
f''(x)=2>0 hence x=9/2 is pt of min
put x=9/2 in the equation x^2-9x-11
x= -125/4 which is the min value of the function f(x)
Answer choice (A)
f'(x)=2x-9
step 2 - put f'(x)=0
2x-9=0
x=9/2 [max/min pt]
step 3 - to check max or min, find f''(x)
- if f''(x)>0 [pt of min]
- if f''(x)<0 [pt of max]
In this case
f''(x)=2>0 hence x=9/2 is pt of min
put x=9/2 in the equation x^2-9x-11
x= -125/4 which is the min value of the function f(x)
Answer choice (A)
General Discussion
14 Jul 2024, 15:31
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One conventional way:
Alter that can be used here: Differential Calculus (for anyone interested)
f(x) = y = x2 - 9x - 11
At the max/min, slope of the curve i.e., dy/dx = 0
At max/min, dy/dx = 2x-9 = 0
So, x = 9/2 is a max/min point.
If d2y/dx2 (differentiate again) > 0, then we are dealing with a minima point. Which is what we see here. d2y/dx2 = 2 > 0. Meaning x = 9/2 is the point at which this curve hits minimum value.
What is this min value? f(9/2) = -125/4. Choice A.
___
Harsha
Enthu about all things GMAT | Exploring the GMAT space | My website: gmatanchor.com
GMAT-Club-Forum-od79vddk.png [ 268.56 KiB | Viewed 850 times ]
Alter that can be used here: Differential Calculus (for anyone interested)
f(x) = y = x2 - 9x - 11
At the max/min, slope of the curve i.e., dy/dx = 0
At max/min, dy/dx = 2x-9 = 0
So, x = 9/2 is a max/min point.
If d2y/dx2 (differentiate again) > 0, then we are dealing with a minima point. Which is what we see here. d2y/dx2 = 2 > 0. Meaning x = 9/2 is the point at which this curve hits minimum value.
What is this min value? f(9/2) = -125/4. Choice A.
___
Harsha
Enthu about all things GMAT | Exploring the GMAT space | My website: gmatanchor.com
Attachment:
GMAT-Club-Forum-od79vddk.png [ 268.56 KiB | Viewed 850 times ]
