3.8 Derivative Review

Front

What is the derivative of f(x) = x^4 + 4x^3 - 2x^2?

Back

f'(x) = 4x^3 + 12x^2 - 4x

Front

At which x-value is f continuous but not differentiable?

Back

a

Front

How many derivatives can you take of a function?

Back

Until you can no longer derive it.

Front

Find the derivative of y = 2x^-1.

Back

y' = -2x^-2.

Front

Find the second derivative of f(x) = 2x - 5x^6.

Back

f''(x) = -150x^4.

Front

What is the power rule for differentiation?

Back

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

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 defined derivative at that point.

Front

What is the difference between continuity and differentiability?

Back

Continuity means the function is unbroken at a point; differentiability means the function has a defined slope (derivative) at that point.

Front

What is the product rule for differentiation?

Back

If u(x) and v(x) are functions, then (uv)' = u'v + uv'.

Front

What is the quotient rule for differentiation?

Back

If u(x) and v(x) are functions, then (u/v)' = (u'v - uv')/v^2.