For the function $f (x) = 8 x^{2} - 3 x + 5$ , find $f^{''} (x)$ . Then find $f^{''} (0)$ and $f^{''} (5)$ .
$f^{''} (x) = ◻ ($ Simplify your answer.)
Select the correct choice below and fill in any answer boxes in your choice.
A. $f^{''} (0) = ◻$ (Simplify your answer.)
B. $f^{''} (0)$ is undefined.

Select the correct choice below and fill in any answer boxes in your choice.
A. $f^{''} (5) = ◻$ (Simplify your answer)
B. $f^{''} (5)$ is undefined.

Answer

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Answer

So, the answers are: $f^{″} (0) = 16$ and $f^{″} (5) = 16$ .

Steps

Step 1 ：Find the first derivative of the function, $f^{'} (x)$ . The derivative of $x^{2}$ is $2 x$ , the derivative of $x$ is $1$ , and the derivative of a constant is $0$ . So, $f^{'} (x) = 2 * 8 x - 3 + 0 = 16 x - 3$ .

Step 2 ：Find the second derivative of the function, $f^{″} (x)$ . The derivative of $x$ is $1$ , and the derivative of a constant is $0$ . So, $f^{″} (x) = 16 - 0 = 16$ .

Step 3 ：Find $f^{″} (0)$ and $f^{″} (5)$ . Since $f^{″} (x)$ is a constant, $f^{″} (0) = f^{″} (5) = 16$ .

Step 4 ：So, the answers are: $f^{″} (0) = 16$ and $f^{″} (5) = 16$ .

Answer

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