QuestionFor the function $f(x)=2 x^{3}-5 x^{2}+7 x+1$, find $f^{\prime \prime}(x)$. Then find $f^{\prime \prime}(0)$ and $f^{\prime \prime}(7)$
To find $f^{\prime \prime}(x)$, first find $f^{\prime}(x)$. $$f^{\prime}(x)=$$

Studdy Solution
Evaluate $f''(x)$ at $x = 7$:
$$f''(7) = 12(7) - 10$$ $$f''(7) = 84 - 10$$ $$f''(7) = 74$$
The second derivative of the function is $f''(x) = 12x - 10$. The values are $f''(0) = -10$ and $f''(7) = 74$.