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For the function
f(x)=x^(2)-4, find the slope of the tangent line at
x=1.
Answer:

For the function $f(x)=x^{2}-4$ , find the slope of the tangent line at $x=1$ . $\newline$ Answer:

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Find the slope of a tangent line using limits

Full solution

Q. For the function

f(x)=x^{2}-4

, find the slope of the tangent line at

x=1

.

\newline

Answer:

Calculate Derivative: To find the slope of the tangent line at a specific point on 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 $f(x) = x^2 - 4$ . To find its derivative, we use the power rule, which states that the derivative of $x^n$ is $n\cdot x^{(n-1)}$ . Applying this rule to $x^2$ , we get $2\cdot x^{(2-1)} = 2x$ . The derivative of a constant is $0$ , so the derivative of $-4$ is $0$ .
Evaluate at $x=1$ : The derivative of $f(x) = x^2 - 4$ is $f'(x) = 2x$ . Now we need to evaluate this derivative at $x = 1$ to find the slope of the tangent line at that point.
Find Slope at $x=1$ : Substitute $x = 1$ into the derivative $f'(x) = 2x$ to find the slope at $x = 1$ . So, $f'(1) = 2\times1 = 2$ .
Conclusion: The slope of the tangent line to the function $f(x) = x^2 - 4$ at $x = 1$ is $2$ .

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