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
