Find the second derivative of the polynomial. f(x) = -12x^2 Write your answer as a polynomial in x or as a constant. Simplify any fractions. (x) = ______

Find First Derivative: First, we need to find the first derivative of the polynomial f(x) = -12x^2. Using the power rule, which states that the derivative of x^n is n*x^(n-1), we calculate: f'(x) = -12 * 2x^(2-1) = -24x Calculate First Derivative: Next, we find the second derivative by differentiating f'(x) = -24x again. Applying the power rule: f''(x) = -24 * 1x^(1-1) = -24

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Find the second derivative of the polynomial. $\newline$ $f(x) = -12x^2$ $\newline$ Write your answer as a polynomial in $x$ or as a constant. Simplify any fractions. $\newline$ $f''(x) =$ ______

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Calculus

Find higher derivatives of polynomials

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Q. Find the second derivative of the polynomial.

\newline

f(x) = -12x^2

\newline

Write your answer as a polynomial in

x

or as a constant. Simplify any fractions.

\newline

f''(x) =

______

Find First Derivative: First, we need to find the first derivative of the polynomial $f(x) = -12x^2$ . Using the power rule, which states that the derivative of $x^n$ is $n\cdot x^{(n-1)}$ , we calculate: $\newline$ $f'(x) = -12 \cdot 2x^{(2-1)} = -24x$
Calculate First Derivative: Next, we find the second derivative by differentiating $f'(x) = -24x$ again. Applying the power rule: $\newline$ $f''(x) = -24 \times 1x^{(1-1)} = -24$