Increasing and decreasing values

[muted summit]

Why is C wrong here? I understand why A is correct but i dont know what makes C wrong.

[muted summit]

If we look at a general quadratic equation and its graph (parabola), we see that there is no such parabola that can always be increasing (or decreasing). On one side it increases, and on the other it decreases. For this quadratic to always decrease means it isn't a quadratic at all - its linear. For an expression to be linear, a (coefficient of x²) must be 0.
Option a allows for this. Option c, on the other hand, does not include 0 (a is strictly less than 0)

@muted summit does that mean here is d too? For some reason chatgpt says its A but i couldnt see a problem with D

Also thank you🙏

[muted summit]

I see some calculus there so I'll differentiate the function (please understand that ive never actually done calculus in class so tell me if I get something wrong because I always seem to miss something).
f'(x) = 3ax² + 2bx + c
you seem to know that if f(x) is strictly increasing, f'(x)>0
A quadratic is always greater than 0 if:

• Coefficient of x² (3a) > 0
• Discriminant (D) < 0

As I just said, no quadratic can be truly strictly increasing. Option d makes your cubic a quadratic, which cannot be strictly increasing as your question asks.