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

f′(x)=12x2−6x+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 functionsright chevron icon

Full solution

Q. f′(x)=12x2−6x+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}
  1. Substitute xx with −1-1: To find f(−1)f(-1), we need to substitute xx with −1-1 in the function f(x)=12x2−6x+2f(x) = 12x^2 - 6x + 2.\newlineCalculation: f(−1)=12(−1)2−6(−1)+2f(-1) = 12(-1)^2 - 6(-1) + 2\newlinef(−1)=12(1)+6+2f(-1) = 12(1) + 6 + 2\newlinef(−1)=12+6+2f(-1) = 12 + 6 + 2\newlinef(−1)=20f(-1) = 20
  2. Calculate f(−1)f(-1): To find f(2)f(2), we need to substitute xx with 22 in the function f(x)=12x2−6x+2f(x) = 12x^2 - 6x + 2.\newlineCalculation: f(2)=12(2)2−6(2)+2f(2) = 12(2)^2 - 6(2) + 2\newlinef(2)=12(4)−12+2f(2) = 12(4) - 12 + 2\newlinef(2)=48−12+2f(2) = 48 - 12 + 2\newlinef(2)=38f(2) = 38

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