Find dy/dx by Implicit Differentiation: $$x^3 + y^3 = 36$$

The derivative is $$-\frac{x^2}{y^2}$$ .

What is the product rule for differentiation?

If $$u(x)$$ and $$v(x)$$ are functions, then $$\frac{d}{dx}[u(x)v(x)] = u$$ .

What is the quotient rule for differentiation?

If $$u(x)$$ and $$v(x)$$ are functions, then $$\frac{d}{dx}\left[\frac{u(x)}{v(x)}\right] = \frac{u$$ .

What is the Fundamental Theorem of Calculus?

It states that if $$F$$ is an antiderivative of $$f$$ on an interval [a, b], then $$\int_a^b f(x)dx = F(b) - F(a)$$ .

What does it mean for a function to be concave up?

A function is concave up if its second derivative is positive, indicating that the slope of the tangent line is increasing.

What does it mean for a function to be concave down?

A function is concave down if its second derivative is negative, indicating that the slope of the tangent line is decreasing.

What is a critical point in calculus?

A critical point occurs where the derivative is zero or undefined, indicating potential local maxima or minima.

What is the Mean Value Theorem?

If a function is continuous on [a, b] and differentiable on (a, b), then there exists at least one c in (a, b) such that $$f$$ .

What is the limit definition of continuity?

A function $$f(x)$$ is continuous at a point $$c$$ if $$\lim_{x \to c} f(x) = f(c)$$ .

AP Calculus Midterm Review Flashcards

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15 questions

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1.

FLASHCARD QUESTION

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2.

FLASHCARD QUESTION

Front

If a function has a derivative that is negative, what does that tell you?

Back

The function is decreasing.

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