AP Calculus Midterm Review

Front

What is the definition of a limit in calculus?

Back

A limit is a value that a function approaches as the input approaches some value.

Front

What does it mean if f'(x) > 0 over an interval?

Back

It means that the function f(x) is increasing over that interval.

Tags

CCSS.HSF.IF.B.4

Front

What is the formula for the equation of a tangent line at a point (x_0, f(x_0))?

Back

y - f(x_0) = f'(x_0)(x - x_0)

Front

What does the Extreme Value Theorem state?

Back

If a function is continuous on a closed interval, then it has a maximum and minimum value on that interval.

Front

What is the derivative of f(x) = 4x^3 - 10x + 5?

Back

f'(x) = 12x^2 - 10.

Front

How do you find the limit as x approaches a value?

Back

Evaluate the function at values approaching that value from both sides.

Front

What is the difference between a one-sided limit and a two-sided limit?

Back

A one-sided limit approaches a value from one direction (left or right), while a two-sided limit approaches from both directions.

Front

What is the significance of critical points in calculus?

Back

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

Front

What does concave up mean in relation to a function's graph?

Back

A function is concave up if its second derivative is positive, indicating the graph opens upwards.

Front

What does concave down mean in relation to a function's graph?

Back

A function is concave down if its second derivative is negative, indicating the graph opens downwards.