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The gradient of the tangent at P (=1) will be equal to the gradient of the curve at point P (=1). The gradient at a point on a curve is given by dy/dx (the differential). First, differentiate the equation...

It can first be observed that this differential equation is linear, so we can solve it by multiplying the whole equation by the integrating factor. As there is no coefficient in front of the dy/dx term, w...

Stationary points occur when the derivative is = 0Derivative: 2x + 2 = 0, so a stationary point occurs when x = -1y = 1 + 2 - 8 = -5Second derivative = 2Therefore, the stationary point (-1,2) is a minimum...