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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. $f'(1) = -6(1) - 3$ $f'(1) = -6 - 3$ $f'(1) = -9$

More problems from Find the slope of a tangent line using limits

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\frac{d y}{d x}=\frac{-y(y+5)}{x(2 y+5)} \text {. }

\newline

Write the equation of the vertical line that is tangent to the curve.

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Question

Which of the following is a correct interpretation of the expression

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-4+13

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1

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(A) The number that is

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(B) The number that is

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(C) The number that is

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Question

f

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

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. You should round all decimals to

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\newline

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Question

f

f(x)=x^{2}-2 x+3 \cos \left(x^{2}-x\right)

. Use a calculator to write the equation of the line tangent to the graph of

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Question

f

f(x)=x^{2}+x-2 \sin (2 x)

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f

f(x)=x^{3}+\cos \left(2 x^{2}+5\right)

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. You should round all decimals to

3

\newline

Posted 2 months ago

Question

f

f(x)=x^{3}+3-5 \sin \left(x^{2}\right)

. Use a calculator to write the equation of the line tangent to the graph of

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. You should round all decimals to

3

\newline

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