Polynomial and Rational Functions

Functions of a polynomial nature involve mathematical expressions that are the sum of powers, which are multiplied by coefficients across one or more variables. Conversely, a function is considered rational if it can be defined by the proportion of two polynomials. These principles are crucial in both algebra and calculus, serving as the basis to explain numerous mathematical occurrences.

Simplifying Absolute Value Expressions

Find the derivative of the function \(f(x) = x^3 - 4x^2 + 6x - 2\), and then simplify the expression \(|f'(2)|\).
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Solving with Absolute Values

Find the derivative of the function \(f(x) = |x^3 - 4x^2 + 3x - 2|\) and solve for \(x\) when \(f'(x) = 0\)
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Simplifying Radical Expressions

Find the derivative of the function \(f(x) = \frac{4x^3 - 9x^2 + 2x - 1}{\sqrt{x}}\)
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Rationalizing Radical Expressions

Find the derivative of the function \(f(x) = \frac{\sqrt{x^3+1}}{x^2+2}\) and simplify your answer by rationalizing the radical expression.
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Solving Radical Equations

Solve the following Radical Equation: \(\sqrt{x^3 - 4x^2 + 4x - 1} = x - 1\)
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Operations on Rational Expressions

Calculate the derivative of the rational function \(f(x) = \frac{x^3 - 2x^2 + 1}{x^2} \)
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Solving Rational Equations

Solve the rational equation \(\frac{2x^2 - 3x - 2}{x^2 - x - 6} = \frac{4x - 3}{x + 1}\)
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Popular Problems

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