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${:[f^(')(x)=12x^(2)-6x+2" and "],[f(-1)=3.],[f(2)=]:}$

$\begin{array}{l}f^{\prime}(x)=12 x^{2}-6 x+2 \text { and } f(-1)=3 . \\ f(2)=\end{array}$

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Find higher derivatives of rational and radical functions

Full solution

Q.

\begin{array}{l}f^{\prime}(x)=12 x^{2}-6 x+2 \text { and } f(-1)=3 . \\ f(2)=\end{array}

Substitute $x$ with $-1$ : To find $f(-1)$ , we need to substitute $x$ with $-1$ in the function $f(x) = 12x^2 - 6x + 2$ . $\newline$ Calculation: $f(-1) = 12(-1)^2 - 6(-1) + 2$ $\newline$ $f(-1) = 12(1) + 6 + 2$ $\newline$ $f(-1) = 12 + 6 + 2$ $\newline$ $f(-1) = 20$
Calculate $f(-1)$ : To find $f(2)$ , we need to substitute $x$ with $2$ in the function $f(x) = 12x^2 - 6x + 2$ . $\newline$ Calculation: $f(2) = 12(2)^2 - 6(2) + 2$ $\newline$ $f(2) = 12(4) - 12 + 2$ $\newline$ $f(2) = 48 - 12 + 2$ $\newline$ $f(2) = 38$

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