- #1
anemone
Gold Member
MHB
POTW Director
- 3,883
- 115
Let $p(x)$ be a polynomial with real coefficients. Prove that if $p(x)-p'(x)-p''(x)+p'''(x)\ge 0$ for every real $x$, then $p(x)\ge 0$ for every real $x$.
A polynomial is a mathematical expression consisting of variables, coefficients, and exponents. It can have one or more terms, and the exponents must be whole numbers.
A derivative is a mathematical concept that represents the rate of change of a function at a specific point. It is calculated by finding the slope of the tangent line to the function at that point.
The first derivative of a polynomial is the derivative of the polynomial function. It represents the slope of the tangent line to the polynomial at any given point.
The second derivative of a polynomial is the derivative of the first derivative. It represents the rate of change of the slope of the polynomial at any given point.
The third derivative of a polynomial is the derivative of the second derivative. It represents the rate of change of the rate of change of the slope of the polynomial at any given point.