It is easier to solve the question this way:
$e^x = kx^2 \implies \dfrac{e^x}{x^2}= k$
We want this equation to have $3$
solutions.
For $f(x)= \dfrac {e^x}{x^2}$
$f'(x)= \dfrac{(x-2)e^x}{x^3}$
Clearly, $f(x)$ is increasing for $x>2$ , decreasing for x $\in (0,2)$ and increasing for $x<0$...
@Abcd spreadsheets have lots of extra functionality. e.g. in this case I can easily put the constant k in a cell so I can quickly change its value and see what happens.
It is easier to solve the question this way:
$e^x = kx^2 \implies \dfrac{e^x}{x^2}= k$
We want this equation to have $3$
solutions.
For $f(x)= \dfrac {e^x}{x^2}$
$f'(x)= \dfrac{(x-2)e^x}{x^3}$
Clearly, $f(x)$ is increasing for $x>2$ , decreasing for x $\in (0,2)$ and increasing for $x<0$...
