- #1
sparkle123
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Why is f(x)=(x-3)^2/(x-6) not concave up for x>6?
It looks like it is from the graph.
It looks like it is from the graph.
The equation for F(x) is (x-3)^2/(x-6).
A function is concave up if its graph curves upwards, resembling a smiley face. This means that the function is increasing at an increasing rate.
If the second derivative of F(x) is positive for all values of x greater than 6, then F(x) is concave up. In this case, the second derivative is 2/(x-6)^3, which is always positive for x>6.
The value of x=6 is a critical point for the function F(x), meaning that it is not defined at this point. Therefore, to determine the concavity of F(x), we must look at values of x greater than 6.
The concavity of F(x) can be shown on a graph by plotting points for various values of x greater than 6 and observing the direction of the curve. Alternatively, the graph can be plotted using a graphing calculator or software to see the concave up shape.