What's the gradient of the curve y=x^3+2x^2 at the point where x=2?
Gradient is change in y divided change in x.As the change shrinks to effectively nothing (as we want to gradient at a point, not between points), we use dy/dx (the derivative of y with respect to x), to work out the gradient at any point.For each term, the coefficient of x is multiplied by the power, and the power is subtracted by one.dy/dx=3x^2+4xThis is a general equation for the gradient at any point.We then substitute in x=2 to work out the gradient at our desired point.Gradient = 3*(2^2) + 42 = 34 + 4*2 = 12 + 8 = 20
ZI
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