First and second derivative question

The derivative of y is the slope of the tangent line to the graph of y= f(x).

At point A the tangent line is horizontal so the slope, and the derivative of y, is 0. At point B, the tangent line is sloping downward so the slope, and the derivative of y, is negative. At point C, the tangent line is vertical so the slope, and the derivative of y is undefined. Those are what you have.

The second derivative is a little more subtle. It is the rate at which the first derivative is changing. At point A the derivative was 0 and at point B the derivative was negative so the derivative is decreasing in value. The second derivative is negative. At point C the derivative does not exist but just before C the derivative has a very large negative value. The second derivative is still negative. At C, since the first derivative is undefined the second derivative is also undefined. That is, again, exactly what you have.

Well done!

The only improvement you need to make now is to have sufficient confidence in yourself that you don't need to ask!
 
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