Early differentiation question help please

Find the coordinates of the point of intersection of the tangents to the graph of y = x ^ 2 at the points at which it meets the line with equation y = x + 2.

Can anyone guide me step by step i hjave no clue, i dont even understand the question!! tanks

The question is asking you to find the point at which two tangent lines intersect. These two lines are the tangents of y = x² when y intersects with y=x+2.

First you have to find the intersection points of x² and x+2. Set them equal to each other;
x² = x + 2
x² - x - 2 = 0
(x - 2)(x + 1) = 0
x = 2, x = -1

So when x=-1 and x=2, x² intersects with x+2.
Evaluate y for each of these values to find the specific points. These will be used for finding the equation of the tangent lines.
y = x² = (-1)² = 1
(-1, 1)
y = x² = (2)² = 4
(2, 4)

Find the equations of the tangent lines at these two points. For this, you need to find the derivative of y=x², which you should know by now is the slope for all x:
dy/dx = 2x

Plug in -1 to find the slope of the tangent line at x=-1:
2(-1) = -2

Now plug in 2 to find slope of tangent at x=2:
2(2) = 4

Use the point-slope formula to find the equations of the tangent lines:
y - y1 = m(x - x1),
where (x1,y1) is the coordinate point and m is the slope (the value of the derivative at each x value).

tangent line at x=-1:
y - 1 = -2(x - (-1))
y = -2x - 1

tangent line at x=2:
y - 4 = 4(x - 2)
y = 4x - 4

Now find the intersection point of the two tangent line by setting them equal to each other:
-2x - 1 = 4x - 4
-6x = -3
x = 1/2

Plug x=1/2 into either tangent line equation. I'll do it with both to check.
-2(1/2) - 1 = -1 - 1 = -2
4(1/2) - 4 = -2

Answer:
(x, y) = (1/2, -2)

So first differentiate y = x ^ 2 to get y=2x ( you know that this is the tangent formula for y = x ^ 2)