Calculus

# Graphical Interpretation of Higher Order Derivatives

In the above diagram, the red curve is the graph of a function $f,$ and the blue curve is the graph of its first derivative $f'.$ What is the relationship between $f'(-1)$ and $f''(1) ?$

Given the graph of $y=f''(x)$ above, which of the following is a possible graph of $y=f(x)?$

Given the graph of $y=f(x)$ above, which of the following is a possible graph of $y=f''(x)?$

Given the graph of $y=f(x)$ above, which of the following is a possible graph of $y=f''(x)?$

Given the graph of $y=f(x)$ above, which of the following is a possible graph of $y=f''(x)?$

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