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For the function
f(x)=2x-6, find the slope of the tangent line at
x=-6.
Answer:

For the function $f(x)=2 x-6$ , find the slope of the tangent line at $x=-6$ . $\newline$ Answer:

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Find the slope of a tangent line using limits

Full solution

Q. For the function

f(x)=2 x-6

, find the slope of the tangent line at

x=-6

.

\newline

Answer:

Calculate Derivative: To find the slope of the tangent line to the function at a given point, 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 $f(x) = 2x - 6$ , the derivative $f'(x)$ is the constant $2$ , because the derivative of $2x$ with respect to $x$ is $2$ , and the derivative of a constant $-6$ is $0$ . $\newline$ Calculation: $f'(x) = \frac{d}{dx} (2x - 6) = 2$
Find Slope at $x = -6$ : Since the derivative $f'(x)$ is constant and equal to $2$ , the slope of the tangent line at any point $x$ is also $2$ . This means that the slope of the tangent line at $x = -6$ is $2$ . $\newline$ Calculation: Slope at $x = -6$ is $f'(-6) = 2$

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