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For the function
f(x)=x^(2)+5, find the slope of the tangent line at
x=5.
Answer:

For the function $f(x)=x^{2}+5$ , find the slope of the tangent line at $x=5$ . $\newline$ Answer:

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Find the slope of a tangent line using limits

Full solution

Q. For the function

f(x)=x^{2}+5

, find the slope of the tangent line at

x=5

.

\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. $\newline$ For the function $f(x) = x^2 + 5$ , we will find the derivative $f'(x)$ .
Find Derivative of Function: The derivative of $x^2$ with respect to $x$ is $2x$ , and the derivative of a constant like $5$ is $0$ . So, the derivative of $f(x) = x^2 + 5$ is $f'(x) = 2x + 0$ , which simplifies to $f'(x) = 2x$ .
Evaluate Derivative at $x=5$ : Now we need to evaluate the derivative at $x = 5$ to find the slope of the tangent line at that point. $\newline$ We substitute $x$ with $5$ in the derivative $f'(x) = 2x$ . $\newline$ $f'(5) = 2 \times 5$
Calculate Slope at $x=5$ : Calculating the value of $f'(5)$ gives us: $\newline$ $f'(5) = 2 \times 5 = 10$ $\newline$ So, the slope of the tangent line at $x = 5$ is $10$ .

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