Find the stationary point of the function f(x) = x^2 +2x + 5
We can find stationary points of functions by using differentiation, we start this by assessing each term individually, we start with the first term x2, we first start by taking the power term (2 in this case) and multiplying the x term by this value, this gives us 2x2, we then subtract 1 from the power term which gives us 2x1 or more simply 2x. The next term is 2x1 we do the same process, which gives us 2x0 which simplifies to 2(1) and then 2. Finally the last term is 5 which differentiates to 0.The finally differential is f(x) = 2x + 2, to find the stationary point we evaluate this function at 0, 2x + 2 = 0, this solves to 2x = -2 and then simplifies to x = -1, this is the x value for stationary point however we need to find the y co-ordinate as well, we do this by putting this x value back into the original function, f(-1) = (-1)2 + 2(-1) + 5 = 4. This gives us the co-ordinate (-1,4).The stationary point for this function is (-1.4)
