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If y= 4 + (x - 3)^2, then y is lowest when x =

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Bunuel
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If y= 4 + (x - 3)^2, then y is lowest when x = [#permalink] New post   17 Sep 2018, 00:31
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If y= 4 + (x - 3)^2, then y is lowest when x =

A. 14
B. 13
C. 0
D. 3
E. 4
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D
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Chethan92
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Re: If y= 4 + (x - 3)^2, then y is lowest when x = [#permalink] New post   17 Sep 2018, 00:37
\((x-3)^2\) is always positive.

minimum value of this expression is 0. So x = 3.

then y = 4.

D is the answer.
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Re: If y= 4 + (x - 3)^2, then y is lowest when x = [#permalink] New post   17 Sep 2018, 01:34
Bunuel wrote:
If y= 4 + (x - 3)^2, then y is lowest when x =

A. 14
B. 13
C. 0
D. 3
E. 4



we are looking for the lowest value of y.

y has 2 parts.

1. 4
2. \(( x - 3)^2.\)

we have nothing to do with 4 but we can curb the value of\((x - 3)^2\).

x = 3 will give us the nothing in \((x-3)^2\) .

Negative value will change the scenario. \((x-3)^2\) always gives us positive value.

The best answer is D.
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If y=4+(x-3)^2, then y is least [#permalink] New post   30 Oct 2018, 08:48
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y=4+(x-3)^2

y is the sum of 2 positive numbers

4 is the first one and (x-3)^2 is the second one.

If we are searching the least value of y, we should search the value of x that gives us the least value of (x-3)^2...which is clearly 3.

Click Here to see a similar problem that i solved on my channel
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If y=4+(x-3)^2, then y is least [#permalink] New post   30 Oct 2018, 08:52
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OA:D

\(y=4+(x-3)^2\)

\({(x-3)^2}\geq{0}\)

Least value of \((x-3)^2\) is \(0\) at \(x=3\).

Least value of \((x-3)^2\) will lead to least value of \(y\) at \(x=3\).
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Re: If y=4+(x-3)^2, then y is least [#permalink] New post   30 Oct 2018, 09:19
putting 3 in the eq- y=4+(x-3)^2
y=4 (least)

Ans- (D)
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Re: If y= 4 + (x - 3)^2, then y is lowest when x = [#permalink] New post   13 Sep 2019, 23:25
Bunuel wrote:
If y= 4 + (x - 3)^2, then y is lowest when x =

A. 14
B. 13
C. 0
D. 3
E. 4


Given: y= 4 + (x - 3)^2

Asked: y is lowest when x = ?

y= 4 + (x - 3)^2
Since (x-3)^2 >=0
y is lowest when (x-3)^2 =0 or x = 3

IMO D
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If y= 4 + (x - 3)^2, then y is lowest when x = [#permalink] New post   05 Apr 2024, 09:20
Kinshook wrote:
Bunuel wrote:
If y= 4 + (x - 3)^2, then y is lowest when x =

A. 14
B. 13
C. 0
D. 3
E. 4

Given: y= 4 + (x - 3)^2

Asked: y is lowest when x = ?

y= 4 + (x - 3)^2
Since (x-3)^2 >=0
y is lowest when (x-3)^2 =0 or x = 3

IMO D

 

­I do understand this approach. But I was trying to approach it using calculus (I know it's not required to use calculus on the test) and from what I know, the first derivative of a function is supposed to give the maximum of value of a function. However I tried this and I got x = 3 as my maximizer value of x.

And I looked up elsewhere online that the 2nd derivative equated to zero gives you the minimizer value of x. But I just didn't get any x value as that disappears in the 2nd derivate to leave only 2 as the result.

Would appreciate any clarification on this.­
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If y= 4 + (x - 3)^2, then y is lowest when x = [#permalink]
05 Apr 2024, 09:20
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