Find dy/dx at (2, 2) for the curve x^2 + 4y^2 = 20.

Derivatives & Second-Order Derivatives · Question 31 of 96

Question 31

EasyOriginal question

Find $\frac{dy}{dx}$ at $(2, 2)$ for the curve $x^2 + 4y^2 = 20$ .

-4

Correct answerYour answer

-1

Correct answerYour answer

- \frac{1}{4}

Correct answerYour answer

\frac{1}{4}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

Differentiate term by term: $2x + 8y\frac{dy}{dx} = 0$ , so $\frac{dy}{dx} = -\frac{x}{4y}$ .
At $(2, 2)$ : $-\frac{2}{8} = -\frac{1}{4}$ .

Worth noting

$-1$ is $-\frac{x}{y}$ , the circle's slope: the 4 in front of $y^2$ was lost.

Ten questions from Derivatives & Second-Order Derivatives, at your own pace.

Ten questions from Derivatives & Second-Order Derivatives, at your own pace.