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12345678

Junior Member
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Mar 30, 2013
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Hello, I was wondering if anybody could help see where I’m going wrong.
I need to find the point on the curve (x value is what I’m having trouble with) Y = √X when the gradient is 1/4.
So I first rewrote Y = √X to Y = X^1/2
I then differentiated this…
dy/dx = ½ X ^(-1/2)
We are told dy/dx = ¼
So 1/2X^(-1/2) = ¼
Rewriting this : ½ (1/X²) = ¼
Dividing by ½ gives: 1/X² = ½
As both numbers have a numerator we can compare the denominators…
X² = 2
X = √2
However, X should equal 4—anybody see why?


 
12345678 said:
Hello, I was wondering if anybody could help see where I’m going wrong.
I need to find the point on the curve (x value is what I’m having trouble with) Y = √X when the gradient is 1/4.
So I first rewrote Y = √X to Y = X^1/2
I then differentiated this…
dy/dx = ½ X ^(-1/2)
We are told dy/dx = ¼
So 1/2X^(-1/2) = ¼
Rewriting this : ½ (1/X²) = ¼
Dividing by ½ gives: 1/X² = ½
As both numbers have a numerator we can compare the denominators…
X² = 2
X = √2
However, X should equal 4—anybody see why?
Click to expand...

\(\displaystyle \frac{1}{2}x^{-1/2} = \dfrac{1}{2\sqrt{x}}\)

Also, while this is no longer relevant to your problem, you should know that \(\displaystyle x^2=2\) gives \(\displaystyle x=\pm \sqrt{2}\), not just 2.
 
daon2 said:
\(\displaystyle \frac{1}{2}x^{-1/2} = \dfrac{1}{2\sqrt{x}}\)

Also, while this is no longer relevant to your problem, you should know that \(\displaystyle x^2=2\) gives \(\displaystyle x=\pm \sqrt{2}\), not just 2.
Click to expand...

Cheers for the reply, I got confused with X^-2 which = 1/X^2.
I understand that X^-1/2 = 1 / √X (as 1 is the power and 2 is the root) but why does the ½ in front of the X make it 2√X ?

 
12345678 said:
Cheers for the reply, I got confused with X^-2 which = 1/X^2.
I understand that X^-1/2 = 1 / √X (as 1 is the power and 2 is the root) but why does the ½ in front of the X make it 2√X ?
Click to expand...

\(\displaystyle \frac{a}{b} \cdot \frac{c}{d} = \frac{a\cdot c}{b\cdot d}\)
 
Silly mistake: ROOT X = 2

Squaring both sides X = 4

Cheers to all who replied
 
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