5.0 3 points)b Identify the graphs A (blue), B(red) and C (green) as the graphs

Question

5.0 3 points)b Identify the graphs A (blue), B(red) and C (green) as the graphs of a function f(r) and its derivatives f (z) and "() (Clicking on the sketch will give you a version of the picture in a separate window) is the graph of the function, (x) is the graph of the function's ftirst derivative. f(a) is the graph of the function's second derivative. f(z) Hint Remember that "(z) is itself a function, and we can tind the derivative of the function f(a), which is called the second derivative of the tunction (a) and denoted by "()

Explanation / Answer

C(green) is the graph of function f(x) which is a cubic polynomial (degree 3 polynomial).

On differentiating f(x), f'(x) will be a degree 2 polynomial.

B(Red) is the graph of function f'(x) which is a quadratic polynomial (degree 2 polynomial).

On differentiating f'(x), f''(x) will be a degree 1 polynomial.

A(Blue) is the graph of function f''(x) which is a straight line (degree 1 polynomial).

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