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Lauren Stendell

Answered question

2022-06-22

Find the derivative of the following function at x = 12.

f(x) = 4x2

Vasquez

Expert2023-05-22Added 669 answers

To find the derivative of the function

f (x) = 4 x^{2}

and evaluate it at

x = 12

, we'll use the power rule of differentiation. The power rule states that if we have a function of the form

f (x) = a x^{n}

, where

a

and

n

are constants, the derivative is given by:

\frac{d}{d x} (f (x)) = n \cdot a \cdot x^{n - 1}

.
Applying the power rule to the function

f (x) = 4 x^{2}

, we have:

\frac{d}{d x} (4 x^{2}) = 2 \cdot 4 \cdot x^{2 - 1}

.
Simplifying the expression, we get:

\frac{d}{d x} (4 x^{2}) = 8 x

.
Now, to find the derivative at

x = 12

, we substitute

x = 12

into the derivative expression:

\frac{d}{d x} (4 x^{2}) |_{x = 12} = 8 \cdot 12

.
Calculating the value, we have:

\frac{d}{d x} (4 x^{2}) |_{x = 12} = 96

.
Therefore, the derivative of the function

f (x) = 4 x^{2}

x = 12

96

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