# Maxima and Minima of a function

by n0_3sc
Tags: function, maxima, minima
 P: 32 Maxima and Minima of a function But there is also possibility to estimate. If you solve some elementary function, for example: $$f(x)=x^2+3x+2$$ You can transform it to form: $$f(x)+\frac{1}{4}=\left(x+\frac{3}{2}\right)^2$$ So now you are able to find a minimum: $$\min_{x\in\mathbb{R}}f(x)=-\frac{1}{4}$$
 Quote by lukaszh But there is also possibility to estimate. If you solve some elementary function, for example: $$f(x)=x^2+3x+2$$ You can transform it to form: $$f(x)+\frac{1}{4}=\left(x+\frac{3}{2}\right)^2$$ So now you are able to find a minimum: $$\min_{x\in\mathbb{R}}f(x)=-\frac{1}{4}$$
Well if you are working with quadratics a lot you should know that the min/max is going to be at $$\left(\frac{-b}{2a}, f\left(\frac{-b}{2a}\right)\right)$$