Power Function Calculator

What Is a Power Function Calculator?

A power function has the form f(x) = a x^n, where a is the coefficient and n is the exponent. The Power Function Calculator evaluates the function at any x, finds its derivative, solves for x given a target output, and lists sample points. It is useful for algebra, calculus, and curve sketching.

How the Math Works

The function and its derivative use the power rule:

$$f(x) = a x^{n}$$

$$f'(x) = n a x^{n-1}$$

Solving f(x) = y for the input gives the nth root form, which needs a nonzero coefficient and exponent:

$$x = \left(\frac{y}{a}\right)^{1/n}$$

Worked Example

Take f(x) = 2x cubed and evaluate it at x = 4. The function value is 128 and the derivative is 96:

$$f(4) = 2 \times 4^{3} = 128, \quad f'(4) = 3 \times 2 \times 4^{2} = 96$$

Solving f(x) = 4 gives x = the cube root of 2, about 1.2599, the input that makes the function equal the chosen target.

Related free tools

For exponent arithmetic, use the Exponent Calculator. The Exponential Function Calculator covers e raised to x, and the Inverse Function Calculator handles general inverses.