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# Answer to Question #6039 in Algebra for Jon

Question #6039
If you are provided with a quadratic function, how can you determine if there is a minimum or maximum function value? How do you compute this value?
A value of x at which the function has either a maximum or a minimum is called a critical value.
The critical values determine turning points, at which the tangent is parallel to the x-axis.& The critical values - if any - will be the solutions to the equation& f '(x) =& 0. In case of quadratic function its minimum(or maximum) will be in its vertex. Quadratic function will have minimum if& branches of its graph(parabola)are directed upwords and& minimum otherwise. For example, let's consider function f(x)=x^2+4x
Then its first derivative f'(x)=2x+4
2x+4=0 =>x=-2
f_min(x)=f(-2)=4-8=-4 - minimum value of function, x=-2 - point of minimum
Let's verify our calculations. Take a look at the graph of considered function:

As you can see from tha graph, function has its minimum at the point x=-2 and value of minimum is -4. The point of minimum is in the vertex of parabola

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