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The turning point of a curve is the point at which the gradient is 0 as from there it stops rising and starts falling or vice versa. To find this we differentiate y with respect to x (dy/dx) to find the g...

We argue using the discriminant of a quadratic polynomial. For a quadratic ax^2 + bx + c=0, the discriminant D is D = b^2 - 4ac. When this quadratic has two distinct real roots, we have that D > 0. So ...

I don't understand why the function "f(x)=x^2 for all real values of x" has no inverse. Isn't sqrt(x) the inverse?
I like to think of a function a bit like a machine. It takes in a number, ...

Let u=exp(2x) and v'=cos(8x)From these you can obtain u' and vu=2exp(2x) and v=1/8 sin(8x)Formula: integral(uv'dx)=uv-integral(vu'dx)=1/8 exp(2x)sin(8x)-integral(1/4 sin(8x)exp(2x))=1/8exp(2x)sin(8x)+1/16...