I want to make sure you understand that absolute value is the distance from zero. It isn't a value; it is a distance.
For example,
6 and -6 both are 6 units from zero. They are opposites on the number line.
8 and -8 are both 8 units from zero. They are opposites on the number line.
But, if you have a negative sign outside the absolute value signs, like so:
-|6| The distance would be 6. But then, since it's outside the signs, it would be -6.
So, yes, wit the signs by itself the absolute value (or distance from zero) is always non-negative.
I hope this helps!
~kaikers
The right option is (c). The Mean Value Theorem does not apply since f(x) is not differentiable on (-1,8). Because the derivative of f is 2/3 x^(-1/3) which is undefined at x=0.So, that would imply that it is not differentiable along the interval.
-c +4d
Step-by-step explanation:
![8c - 4d + 8d + 9c - 18c](https://tex.z-dn.net/?f=8c%20-%204d%20%2B%208d%20%2B%209c%20-%2018c)
Group like terms and simplify
![8c + 9c - 18c - 4d + 8d \\ - c + 4d](https://tex.z-dn.net/?f=8c%20%2B%209c%20-%2018c%20-%204d%20%2B%208d%20%5C%5C%20%20-%20c%20%2B%204d)