Apentix/AP Calculus AB/Unit 5: Analytical Applications of Differentiation/Question

AP Calculus ABmediummcq1 pt

What is the slope of the line tangent to $x^2+y^2=25$ at the point $(3,4)$ ?

A.

-\dfrac{3}{4}

B.

\dfrac{3}{4}

C.

-\dfrac{4}{3}

D.

\dfrac{4}{3}

Explanation

Core Concept

Differentiating gives $2x+2y\cdot y'=0$ , so $y'=-x/y=-3/4$ at $(3,4)$ .

Correct Answer

A $-\dfrac{3}{4}$

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?
easyIf $x^2+y^2=25$, then $\dfrac{dy}{dx}=$
hardA right circular cylinder is inscribed in a right circular cone of height 12 and base radius 6, with the cylinder's base on the cone's base.…

Try a random question →

Practice more AP Calculus AB questions with full explanations

Practice Unit 5: Analytical Applications of Differentiation Questions →