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

AP Calculus ABmediummcq1 pt

At which points does the curve $x^2+y^2=25$ have a horizontal tangent line?

A.

(5,0)

and

(-5,0)

B.

(0,5)

and

(0,-5)

C.

(0,5)

and

(5,0)

D.

(3,4)

and

(-3,-4)

Explanation

Core Concept

A horizontal tangent requires $dy/dx=-x/y=0$ , so $x=0$ with $y\neq 0$ . The points on the curve are $(0,5)$ and $(0,-5)$ .

Correct Answer

B $(0,5)$ and $(0,-5)$

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 $\dfrac{dy}{dx}$?
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 $\dfrac{dy}{dx}=$
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 →