AP Calculus ABhardmcq1 pt

Given the curve defined by the equation $x^2 + xy + y^2 = 7$ , find the slope of the tangent line to the curve at the point $(2, 1)$ .

-5/4

5/4

-4/5

4/5

Explanation

Core Concept

Correct. Using implicit differentiation, $2x + y + xy' + 2yy' = 0$ . Substituting $x=2$ and $y=1$ gives $4 + 1 + 2y' + 2y' = 0$ , which simplifies to $5 + 4y' = 0$ , yielding $y' = -5/4$ .

Correct Answer

A $-5/4$

More Unit 5: Analytical Applications of Differentiation practice questions

hardAt which points does the curve $x^2+xy+y^2=7$ have a vertical tangent line?
hardFor the curve $x^3+y^3=6xy$, what is $\dfrac{dy}{dx}$?
mediumAt which points does the curve $x^2+y^2=25$ have a horizontal tangent line?
mediumWhat is the slope of the line tangent to $x^2+y^2=25$ at the point $(3,4)$?
easyIf $x^2+y^2=25$, then $\dfrac{dy}{dx}=$

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Given the curve defined by the equation x2+xy+y2=7x^2 + xy + y^2 = 7x2+xy+y2=7, find the slope of the tangent line to the curve at the point (2,1)(2, 1)(2,1).

Explanation

Core Concept

Correct Answer

More Unit 5: Analytical Applications of Differentiation practice questions

Given the curve defined by the equation $x^2 + xy + y^2 = 7$ , find the slope of the tangent line to the curve at the point $(2, 1)$ .