Questions: Find the slope of the tangent line to the graph of (f(x)=-x^2+5 x-1) at (x=4). Provide your answer below: [mtan =]

Find the slope of the tangent line to the graph of (f(x)=-x^2+5 x-1) at (x=4). Provide your answer below: [mtan =]
Transcript text: 10:33 15 knewton.com 2.7a Derivatives and Rates of Change... UASTERY 1\% Due Friday, Jan 10, 11:59pm PST CURRENT OBJECTIVE Find the slope of a tangent line using the first limit definition Question Find the slope of the tangent line to the graph of $f(x)=-x^{2}+5 x-1$ at $x=4$. Provide your answer below: \[ m_{\tan }= \] $\square$ Content attribution
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Solution

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Solution Steps

Step 1: Define the Function

We start with the function \( f(x) = -x^2 + 5x - 1 \).

Step 2: Compute the Derivative

Next, we compute the derivative of the function, which is given by \( f'(x) = -2x + 5 \).

Step 3: Evaluate the Derivative at \( x = 4 \)

Finally, we evaluate the derivative at \( x = 4 \): \[ f'(4) = -2(4) + 5 = -8 + 5 = -3 \] Thus, the slope of the tangent line at \( x = 4 \) is \( m_{\tan} = -3 \).

Final Answer

\(\boxed{m_{\tan} = -3}\)

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