Two point that are interaction of the curve $y=2^x$ and $y=-2x^2+2$ are defined as $(x_1,y_1)$ and $(x_2,y_2)$ where $x_2>x_1$. Then which of the following is/are correct.
A) $x_2>\frac{1}{2}$
B) $y_2-y_1<x_2-x_1$
C) $\frac{\sqrt2}{2}<y_1y_2<1$
The correct option is ABC
Based on the figure we conclude that ABC is the correct option
I can only prove that $x_2>\frac{1}{2}$
$y=2^{\frac{1}{2}}=\sqrt2$
$y=-2(\frac{1}{2})^2+2$=$\frac{3}{2}$ there the quadratic equation is greater than exponential equation as quadratic equation is decreasing hence $x_2>\frac{1}{2}$
Rest not able to solve