ap calculus bc flashcard 2.1 - 2.6

Front

What does h'(43) = -11 signify in the context of the function h(t) representing oven temperature?

Back

The oven is cooling at 11 degrees per minute at minute 43.

Front

How do you find the average rate of change for the function w(x) = ln x over the interval [1, 7]?

Back

Front

What does it mean for a function to be continuous but not differentiable at a point?

Back

A function is continuous at a point if it is defined and has no breaks, but it is not differentiable if it has a sharp corner or cusp at that point.

Front

Differentiate the function h(x) = 3x^(5/3) - 6x^(1/6) + 3x.

Back

h'(x) = 5x^(2/3) - x^(-5/6) + 3.

Front

Evaluate the limit: @@ ext{lim}_{x ightarrow2}rac{x^2-4}{x-2}@@.

Back

The limit evaluates to 4.

Front

What is the definition of the derivative of a function at a point?

Back

The derivative of a function at a point is the limit of the average rate of change of the function as the interval approaches zero.

Front

What is the significance of a negative derivative value?

Back

A negative derivative indicates that the function is decreasing at that point.

Front

How do you determine if a function is continuous at a point?

Back

A function is continuous at a point if the limit as x approaches the point equals the function's value at that point.

Front

What is the power rule for differentiation?

Back

The power rule states that if f(x) = x^n, then f'(x) = n*x^(n-1).

Front

What does it mean for a function to be differentiable?

Back

A function is differentiable at a point if it has a derivative at that point, meaning it has a defined tangent line.