Answer:
Numbers are -2 and 1.
Step-by-step explanation:
Let x be the second number,
⇒ First number = 4 less than twice a second number
= 2 × Second number - 4
= 2x - 4
Thus, the product of first and second number is,
![f(x) = x(2x-4)](https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%282x-4%29)
![\implies f(x) = 2x^2 - 4x](https://tex.z-dn.net/?f=%5Cimplies%20f%28x%29%20%3D%202x%5E2%20-%204x)
Differentiating with respect to x,
![f'(x) = 4x -4](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%204x%20-4)
Again differentiating with respect to x,
![f''(x) = 4](https://tex.z-dn.net/?f=f%27%27%28x%29%20%3D%204)
Now, for maximum or minimum,
![f'(x)=0](https://tex.z-dn.net/?f=f%27%28x%29%3D0)
![\implies 4x - 4 = 0\implies 4x = 4\implies x = 1](https://tex.z-dn.net/?f=%5Cimplies%204x%20-%204%20%3D%200%5Cimplies%204x%20%3D%204%5Cimplies%20x%20%3D%201)
Since, for x = 1, f''(x) = Positive,
Therefore, the function f(x) is minimum for x = 1,
⇒ The product is smallest for x = 1,
Hence, the second number = x = 1,
And, first number = 2x - 4 = 2 - 4 = -2