What is the derivative of $$x^{e\text{pi}}$$ ?

$$\frac{d}{dx}[x^{e\text{pi}}] = e\text{pi} \times x^{(e\text{pi}-1)}$$

What are the units of the average rate of change of radius $$r$$ for a deflating balloon?

$$\text{centimeters per second}$$ .

What does it mean if $$f$$ does not exist?

It indicates that there is a cusp or vertical tangent at x=0, meaning the slope of the tangent line cannot be defined.

What is the formula for the average rate of change of a function over an interval [a,b]?

$$\frac{f(b) - f(a)}{b - a}$$ .

What is the definition of a critical point in calculus?

A critical point occurs where the derivative of a function is zero or undefined.

What does the notation $$f$$ represent?

It represents the derivative of the function f with respect to x, indicating the rate of change of f at x.

What is the meaning of $$f$$ ?

It indicates that the function is concave down at the point c, suggesting that the function is decreasing.

What is the relationship between the average rate of change and instantaneous rate of change?

The average rate of change is the slope of the secant line between two points, while the instantaneous rate of change is the slope of the tangent line at a specific point.

What does it mean for a function to be differentiable at a point?

A function is differentiable at a point if it has a defined derivative at that point, meaning it is smooth and has no sharp corners.

AB Sem 1 Final Review Flashcards

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