What is the derivative of the function f(x) = $$x^4 + 4x^3 - 2x^2$$ ?

The derivative is $$4x^3 + 12x^2 - 4x$$ .

What is the derivative of the function f(x) = $$\frac{1}{x^2}$$ ?

The derivative is $$-2x^{-3}$$ .

What is the slope of the normal line to the function f(x) = $$\frac{4\text{sqrt}{x}}{5}$$ at x = 16?

The slope of the normal line is $$-10$$ .

What is the quotient rule for differentiation?

If f(x) = $$\frac{g(x)}{h(x)}$$ , then f'(x) = $$\frac{g$$ .

What is the chain rule for differentiation?

If f(x) = g(h(x)), then f'(x) = g'(h(x))h'(x).

What is the derivative of a constant function?

The derivative of a constant function is 0.

What does it mean if the derivative of a function is positive?

If the derivative is positive, the function is increasing.

What does it mean if the derivative of a function is negative?

If the derivative is negative, the function is decreasing.

What is the second derivative?

The second derivative is the derivative of the derivative, indicating the concavity of the function.

What is the relationship between the first derivative and the slope of a function?

The first derivative gives the slope of the tangent line to the function at any point.

What is the significance of critical points in calculus?

Critical points occur where the derivative is zero or undefined, indicating potential local maxima or minima.

Derivatives

Flashcard

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Mathematics

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11th Grade

•

Practice Problem

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Hard

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CCSS

HSF.IF.B.4, 8.EE.B.5

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FLASHCARD QUESTION

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FLASHCARD QUESTION

Front

Back

FLASHCARD QUESTION

Front

What does the derivative represent in terms of a function's graph?

Back

The derivative represents the slope of the tangent line to the graph of the function.

FLASHCARD QUESTION

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