Calculus

Higher-order Derivatives

Graphical Interpretation of Higher Order Derivatives

         

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

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

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

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

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

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