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Find the slope of the tangent line to the graph of $x = -2y^2 + y + 2$ at $(-1,-1)$ .

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Find tangent lines using implicit differentiation

Full solution

Q. Find the slope of the tangent line to the graph of

x = -2y^2 + y + 2

at

(-1,-1)

.

Find Derivative of $x$ : First, we need to find the derivative of $x$ with respect to $y$ , since the equation is given in terms of $y$ . We use the power rule for differentiation. $\newline$ $\frac{dx}{dy} = \frac{d}{dy}(-2y^2 + y + 2)$ $\newline$ = $-4y + 1$
Evaluate Derivative at $y=-1$ : Next, we evaluate the derivative at the point $y = -1$ to find the slope of the tangent line at that point. $\newline$ $\frac{dx}{dy}$ at $y = -1$ = $-4(-1) + 1$ $\newline$ = $4 + 1$ $\newline$ = $5$

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