Question

The number of points of intersection of the two curves $y=2\sin x$ and $y=5x^2+2x+3$ is

• A. $0$
• B. $1$
• C. $2$
• D. $\infty$

Answer 1

The correct option is A $0$

We know that max value of $y=a\sin x$ wiil be $a$

So maximum value of $y=2\sin x=2$

$y=5x^2+2x+3y^{\prime }=10x+2y^{\prime }=0\Rightarrow 10x+2=0x=-\frac{1}{5}{y}^{\prime \prime }=10$

We see that $y^{\prime \prime }>0$ at $x=\frac{-1}{5}$ so $x=\frac{-1}{5}$ is point of minima; and the Minimum value is given by

$y=5\times {\frac{-1}{5}}^2-2\times \frac{1}{5}+3=\frac{14}{5}$

The minimum value of second function is greater than the maximum value 2 of the first function. So both functions will not intersect each other.