How do you find the gradient of a curve?

Unlike a straight line, the gradient of a curve is not a constant i.e. not one single number. To find the gradient of a curve, you different the equation of the curve. To find the gradient at a specific point you then substitute its x and y values into the gradient equation. For example, for a curve with equation y=4x^2 + 2x -3, you will differentiate each term by multiplying by it's power and then lowering the power by one, like this: 4x^2 becomes (2)(4)(x^1) = 8x, then 2x becomes 2 and -3 becomes 0. Thus the differential is given by: dy/dx = 8x +2. If you wanted to know the gradient at say a point (2,17) then you simply substitute in 2 for x, giving: dy/dx = 8(2)+2 = 18.