examday

/TMUA

Let $f$ be a polynomial with real coefficients.

The integral $I_{p,q}$ where $p<q$ is defined by

Which of the following statements must be true?

• 1. $I_{p,q}=0$ only if $0<p$.
• 2. $f'(x)<0$ for all $x$ only if $I_{p,q}<0$ for all $p<q<0$.
• 3. $I_{p,q}>0$ only if $p<0$.