A curve has the equation y = x^4 - 8x^2 + 60x + 7. What is the gradient of the curve when x = 6?

To find the gradient of any curve, we take the derivative. So in this case, we need to take dy/dx. We do this by multiplying the term by the power on x, and then lowering the power by one. For example, for the first term, x⁴, the power is four, so we multiply x⁴ by four, and the power becomes three, so we have 4x³. We repeat this for all of the terms individually to get dy/dx = 4x³ -16x +60. That gives us the gradient at any point. To get the gradient at x = 6 we need to substitute the value in to the new equation, so we get dy/dx = 4 * 6³ - 16 * 6 + 60 = 828