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The stationary points on a curve of the form y=f(x) are where dy/dx = 0. To find dy/dx, differentiate using the product rule: dy/dx = 7e^x(d/dx(cosx)) + cosx(d/dx(7e^x)) = -sinx(7e^x) + cosx(7e^x). Now se...

I like to separate problems into small steps that are easy to follow. In this example these would be: STEP 1: make y the subject (meaning only y on the Left hand side - LHS); 3y = -5x - 3. STEP 2: divide ...

Because we have a product of two functions of x, our first instinct is to apply integration by parts. Let u = e^(2x) and v' = cos(x). We then integrate v' to find v = sin(x) and differentiate u to find u'...

The first step in finding any turning point is to differentiate. To do this, we muiltiply x by its power and drop the power by 1. so in this senario we multiply the -2x by 2 giving us -4x and the power be...

(a) (i) Use the Factor Theorem to show that x + 3 is a factor of p(x).

The Factor Theorem is derived from the remainder theorem. We know from the remainder theorem that by doing p(x)/(x – a) then w...