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Firstly, we need to differentiate the function of the curve y = x^3 + 2x^2 - 5. Using d/dx (x^n) = nx^(n - 1), we get dy/dx = 3x^2 + 4x. To find the gradient of this curve, we then need to evaluate dy/dx ...

You have a general quadratic of the form: ax^2 + bx + c = 0, where a,b,c are constants (although is consistent for functions). Divide by a (assuming a/=0, this would not be a quadratic in that case):x^2 +...

We know that x²+kx-3k-5<0 for some x for the values the k that we are trying to find.This will only occur when the curve has two distinct intersections with the x-axis. There are two distinct intersect...

(This is a common question in C4, the "hardest" module of the old A level)When differentiating we consider each term one at a time:Differentiating 3x² simply gives us 6x Differentiati...

We are looking for a straight line, so it needs the form y=mx+c. To find our gradient, m, we need the gradient of the curve at the point x=-2, so differentiate the equation: dy/dx=6x²+6x-4, and...