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)