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Question
Find the slope of the line tangent to the graph of
f(x)=-3x^(2)-3x+2 at
x=1.

Question $\newline$ Find the slope of the line tangent to the graph of $f(x)=-3 x^{2}-3 x+2$ at $x=1$ .

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Find the slope of a tangent line using limits

Full solution

Q. Question

\newline

Find the slope of the line tangent to the graph of

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

at

x=1

.

Find Derivative: First, let's find the derivative of $f(x) = -3x^2 - 3x + 2$ . $\newline$ Using the power rule, the derivative $f'(x)$ is: $\newline$ $f'(x) = \frac{d}{dx}(-3x^2) + \frac{d}{dx}(-3x) + \frac{d}{dx}(2)$ $\newline$ $f'(x) = -6x - 3$
Evaluate at $x=1$ : Now, we'll evaluate the derivative at $x=1$ to find the slope of the tangent line. $f'(1) = -6(1) - 3$ $f'(1) = -6 - 3$ $f'(1) = -9$

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