The red line is x^2.
The blue line is 2x (derivative of x^2)
Use a straight (vertical) line and move it along the X axis. Start at, say, x = -2. X on the red graph is 4, but x on the blue graph is -4. The slope of x^2 at x = -2 is -4.
Notice as you move the line from x = -2 to x = 0, the slope (blue line) of x^2 INCREASES to 0. At x = 0, there is no slope on x^2, therefore 2x = 0.
Move the line to the right to x = 1.
x^2 = 1, but the slope is 2.
Move to x = 2. When x = 2, the slope of x^2 is 4, but notice the lines intersect because the slope is also 4.
Now, let's look at the derivative of 2x, which is a constant 2.
No matter what x equals, the slope of 2x is always 2. That's why there's a straight line at 2. x could be 293849238492, but the slope of 2(293849238492) is still 2.
Now put all 3 together:
