How do I determine the second derivative if I have a graph of f(x)?
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The derivative and second derivative are negative at which point?
The derivative is zero at maximums and minimums. If the second derivative is positive at this point, the point is a minimum. If the second derivative is negative at the point, there is a maximum. If the second derivative is zero at the point, the test is inconclusive.
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At A, the derivative is positive, and the second derivative is negative (concave downward).
At B, the derivative is negative, and the second derivative is negative (concave downward).
At C, the derivative is negative, and the second derivative is positive (concave upward).
At D, the derivative is zero, and the second derivative is positive (concave upward).
At E, the derivative is positive, and the second derivative is positive (concave upward).
All this stuff can be surmised from the slope and curvature of the curve at the respective points.