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For the function
f(x)=x^(2)-3, find the slope of the tangent line at
x=12.
Answer:

For the function $f(x)=x^{2}-3$ , find the slope of the tangent line at $x=12$ . $\newline$ Answer:

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Find the slope of a tangent line using limits

Full solution

Q. For the function

f(x)=x^{2}-3

, find the slope of the tangent line at

x=12

.

\newline

Answer:

Calculate Derivative: To find the slope of the tangent line at a specific point on the graph of a function, we need to calculate the derivative of the function. The derivative of a function at a point gives us the slope of the tangent line at that point.
Apply Power Rule: The function given is $f(x) = x^2 - 3$ . To find the derivative of this function, we use the power rule, which states that the derivative of $x^n$ is $n\cdot x^{(n-1)}$ . Applying this rule to our function, we get the derivative $f'(x) = 2\cdot x^{(2-1)} = 2x$ .
Find Slope at $x=12$ : Now that we have the derivative, we can find the slope of the tangent line at $x = 12$ by evaluating the derivative at that point. So we calculate $f'(12) = 2 \times 12$ .
Evaluate Slope: Evaluating $f'(12)$ gives us $2\times12 = 24$ . This is the slope of the tangent line to the function at $x = 12$ .

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