Friday, March 6, 2015

Notice the graph of a quadratic function f(x) = x^2 + 3x  + 8 is a parabola that opens up.  What if you know how to find the vertex but forget how to determine whether the vertex is the maximum or minimum point, therefore not knowing that is opens up or down.  You can take the second derivative and set equal to zero to determine whether the function is concave up or concave down.

The first derivative f'(x) = 2x + 3

Second derivative f"(x) = 2

Notice the second derivative is positive for all values of x therefore the function is concave up, therefore opening up.

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