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dy/dx=2x + 2

Turning point is where dy/dx=0, so when x = -1

When x=-1, y=0.

d^2y/dx^2=2 > 0 therefore minimum.

3e^3x + (9x)e^3x This is a good question because it involves the use of both the chain and product rules of differentiation, as well as the differential of e (all of which occur frequently in Maths A-leve...

Let a be the first term

Let d be the common difference

a + d = 7

S₄ = 4/2 (2a +3d) = 12

Simultaneous equation:

a+d =7 // x 6
4a +6d = 12

Differen...

Firstly, we may simplify the expression by factoring out any constants. In this case 5 can be factored out. 

5 ∫ cos(3x-1) dx 

For the integrand cos(3x -1), we can use a simple u-substitutio...

The first step in this solution is to factorise the equation we have been given into the form (ax+b)(cx+d)=0, where a, b, c and d are constants which we need to determine. If we were to expand the bracket...