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?
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?