Define composite function.

A function formed by applying one function to the results of another; $f(g(x))$ .

Flip to see [answer/question]

Revise later

SpaceTo flip

If confident

All Flashcards

Define composite function.

A function formed by applying one function to the results of another; $f(g(x))$ .

What is implicit differentiation?

A method to find $\frac{dy}{dx}$ when $y$ is not explicitly defined as a function of $x$ .

What is a higher-order derivative?

A derivative of a derivative (e.g., second derivative, third derivative).

Define the first derivative.

The derivative of a function, denoted as $f'(x)$ or $\frac{dy}{dx}$ , representing the slope of the tangent line.

Define the second derivative.

The derivative of the first derivative, denoted as $f''(x)$ or $\frac{d^2y}{dx^2}$ , indicating the concavity of the function.

What is the chain rule formula?

$\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}$

What is the formula for implicit differentiation of $y^n$ with respect to $x$ ?

$\frac{d}{dx}(y^n) = n \cdot y^{n-1} \cdot \frac{dy}{dx}$

How to approximate the derivative using a table?

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

What does a positive first derivative on a graph indicate?

The function is increasing.

What does a negative first derivative on a graph indicate?

The function is decreasing.

What does a positive second derivative on a graph indicate?

The function is concave up.

What does a negative second derivative on a graph indicate?

The function is concave down.

What does a point of inflection on a graph indicate?

The concavity of the function changes at that point; $f''(x) = 0$ or is undefined.

How do you find critical points on a graph?

Look for points where the slope (derivative) is zero or undefined.

How do you determine intervals of increasing/decreasing from a graph?

Identify where the slope (derivative) is positive (increasing) or negative (decreasing).