Applications of Derivatives

Front

What is the derivative of f(x) = 1/x²?

Back

-2x⁻³

Front

How many extrema are present in a function with three turning points?

Back

3

Front

Find the derivative of f(x) = x⁴ + 4x³ - 2x².

Back

4x³ + 12x² - 4x

Front

If a function has a derivative that is positive, what does that indicate about the function?

Back

The function is increasing.

Front

What is the derivative of sin(x)?

Back

cos(x)

Front

What does the first derivative test help determine?

Back

It helps determine local extrema (maxima and minima) of a function.

Front

What is the power rule for differentiation?

Back

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

Front

What does a negative derivative indicate about a function?

Back

The function is decreasing.

Front

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

Back

e^x

Front

How do you find the critical points of a function?

Back

Set the derivative equal to zero and solve for x.