Solve y=-7x² > 0: Finding Values Where Function is Positive

Question

Given the function y=7x2 y=-7x^2

Determine for which values of x the following holds:

f\left(x\right) > 0

Step-by-Step Solution

To solve this problem, let's work through the following steps:

Step 1: Analyze the inequality 7x2>0 -7x^2 > 0 .
Since x20 x^2 \geq 0 for all real x x and x2=0 x^2 = 0 when x=0 x = 0 , we know x2>0 x^2 > 0 when x0 x \neq 0 . However, the expression 7x2 -7x^2 is always less than or equal to zero because multiplying a non-negative x2 x^2 by 7-7 gives a non-positive result.
Therefore, 7x2>0 -7x^2 > 0 cannot be true for any real x x .

Step 2: Conclude based on this analysis.
The only scenario where 7x2 -7x^2 could have been greater than zero is if we had a positive term offsetting it, which is not the case.
Hence, there are no values of x x for which f(x)>0 f(x) > 0 .

The correct answer based on the provided choices is No x.

Answer

x0 x\ne0