$f ( x )$ is a polynomial with real coefficients. The equation $f ( x ) = 0$ has exactly two real roots, $x = - p$ and $x = p$, where $p > 0$. Consider the following three statements: $1 \quad f ^ { \prime } ( x ) = 0$ for exactly one value of $x$ between $- p$ and $p$ 2 The area between the curve $y = f ( x )$, the $x$-axis and the lines $x = - p$ and $x = p$ is given by $2 \int _ { 0 } ^ { p } f ( x ) \mathrm { d } x$ 3 The graph of $y = - f ( - x )$ intersects the $x$-axis at the points $x = - p$ and $x = p$ only Which of the above statements must be true?
& E & 11 & D
$f ( x )$ is a polynomial with real coefficients.
The equation $f ( x ) = 0$ has exactly two real roots, $x = - p$ and $x = p$, where $p > 0$.
Consider the following three statements:
$1 \quad f ^ { \prime } ( x ) = 0$ for exactly one value of $x$ between $- p$ and $p$
2 The area between the curve $y = f ( x )$, the $x$-axis and the lines $x = - p$ and $x = p$ is given by $2 \int _ { 0 } ^ { p } f ( x ) \mathrm { d } x$
3 The graph of $y = - f ( - x )$ intersects the $x$-axis at the points $x = - p$ and $x = p$ only
Which of the above statements must be true?