Find the second derivative of the polynomial. f(x) = 14x^2 Write your answer as a polynomial in x or as a constant. Simplify any fractions. (x) = ______

Identify function and task: First, identify the function given and what is asked. We need to find the second derivative of the polynomial f(x) = 14x^2. Calculate first derivative: Calculate the first derivative of f(x). The derivative of 14x^2 with respect to x is 28x (using the power rule: d/dx of ax^n = n*ax^(n-1)). Calculate second derivative: Now, calculate the second derivative. The derivative of 28x with respect to x is 28 (again using the power rule, this time the derivative of x is 1).

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Find the second derivative of the polynomial. $\newline$ $f(x) = 14x^2$ $\newline$ 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) = 14x^2

\newline

Write your answer as a polynomial in

x

or as a constant. Simplify any fractions.

\newline

f''(x) =

______

Identify function and task: First, identify the function given and what is asked. We need to find the second derivative of the polynomial $f(x) = 14x^2$ .
Calculate first derivative: Calculate the first derivative of $f(x)$ . The derivative of $14x^2$ with respect to $x$ is $28x$ (using the power rule: $\frac{d}{dx}$ of $ax^n = n\cdot ax^{n-1}$ ).
Calculate second derivative: Now, calculate the second derivative. The derivative of $28x$ with respect to $x$ is $28$ (again using the power rule, this time the derivative of $x$ is $1$ ).