How do you determine the concavity of a quadratic function?
2 Answers
For a quadratic function
if
if
For a quadratic function
#f(x)=ax^2+bx+c#
#f'(x)=2ax+b#
#f''(x)=2a#
In any function, if the second derivative is positive, the function is concave up. If the second derivative is negative, the function is concave down.
Since the second derivative of any quadratic function is just
This can be shown graphically:
The function
graph{6x^2+3x-5 [-18.5, 17.54, -10.35, 7.68]}
The function
graph{-1/2x^2-7x+1 [-64.2, 52.83, -24.88, 33.7]}