If tangent to the curve y = √x is parallel to the line y = 8x, then this implies that the tangent to y = √x has the same slope as the line y = 8x. In other words, the derivative (slope) function of y = √x is equal to the slope of the line y = 8x, which is m = 8. Hence y' = 8 once we find y'
y = √x = x^(1/2)
Applying the power rule and simplifying, we find that the derivative is
y' = 1/(2√x)
Now remember that y' must equal 8
1/(2√x) = 8
Multiplying both sides by 2√x, we obtain
1 = 16√x
Dividing both sides by 16, yields
√x = 1/16
But wait a minute, √x = y. Thus 1/16 must be the y-coordinate of the point at which the tangent to y = √x is drawn.
Squaring both sides, yields
x = 1/256
This is the x-coordinate of the point on the curve where the tangent is drawn.
∴ the required point must be (1/256, 1/16)
GOOD LUCK!!!
