For the function ( f(x)=2 x^{3}-5 x^{2}+13 x+2 ), find ( f^{prime prime}(x) ). Then find ( f^{prime prime}(0) ) and ( f^{prime prime}(4) ). ( f^{prime prime}(x)= ) Select the correct choice below and fill in any answer boxes in your choice. A. ( f^{prime prime}(0)= ) (Simplify your answer.) B. ( f^{prime prime}(0) ) is undefined. Select the correct choice below and fill in any answer boxes in your choice. A. ( f^{prime prime}(4)= ) (Simplify your answer.) B. ( f^{prime prime}(4) ) is undefined.
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Given \(f(x) = 2x^3 - 5x^2 + 13x + 2\), the first derivative \(f'(x)\) is found by differentiating each term with respect to \(x\). \[f'(x) = \frac{d}{dx}(2x^3) - \frac{d}{dx}(5x^2) + \frac{d}{dx}(13x) + \frac{d}{dx}(2)\] \[f'(x) = 6x^2 - 10x + 13\] Show more…
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