Calc 3A IC Review

Front

What is the derivative of the function f(x) = x^4?

Back

f'(x) = 4x^3

Front

What is the definition of continuity at a point c?

Back

A function f is continuous at c if lim(f^-) = lim(f^+) = f(c).

Front

How do you calculate displacement from a function over a given interval?

Back

Displacement is calculated by evaluating the definite integral of the function over the interval.

Front

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

Back

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

Front

Find the derivative of the function f(x) = 12 - 8x.

Back

f'(x) = -8

Front

What is the power rule for differentiation?

Back

If f(x) = x^n, then f'(x) = n*x^(n-1).

Front

What is the significance of the limit in the definition of continuity?

Back

The limit ensures that the function approaches the same value from both sides as it approaches c.

Front

What is the relationship between differentiability and continuity?

Back

If a function is differentiable at a point, it is also continuous at that point, but the converse is not necessarily true.

Front

How do you find the derivative of a constant function?

Back

The derivative of a constant function is always zero.

Front

What is the derivative of f(x) = 3x^2 + 5x - 7?

Back

f'(x) = 6x + 5.