Answer:
Step-by-step explanation:
We say that a function is differentiable if it's derivative exists and it is continous over the domain of the original function. Recall that the function |x| is given as |x| = x if
and |x|=-x if x<0. In both cases, we have either the function x or -x, which are one-degree polynomials. So, we can find easily their derivatives. So if f(x) = |x|. Then, we have that
![f'(x) = (x)' = 1 \text{if } x\geq 0](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20%28x%29%27%20%3D%201%20%5Ctext%7Bif%20%7D%20x%5Cgeq%200)
![f'(x) = (-x)' = -1 \text{if } x](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20%28-x%29%27%20%3D%20-1%20%5Ctext%7Bif%20%7D%20x%3C0)
We should check what happens x=0, since that is the point where the definition of f changes. We can check that
and
![\lim_{x\to 0^-} f'(x) = -1](https://tex.z-dn.net/?f=%5Clim_%7Bx%5Cto%200%5E-%7D%20f%27%28x%29%20%3D%20-1)
since this limits are not equal, the derivative is not continous at x=0. Hence, the derivative doesn't exist at x=0.
In this case, we say that |x| is differentiable at any x different from 0.
2 ,It is the numbers at the beginning the zeros dont count so you would just count the numbers above 0 <span>
</span>
Answer:
Lin has 11 acorns ⇒ answer D
He subtract 4 from 7 instead of add 4 to 7
Step-by-step explanation:
- Lin has 4 pinecones and some acorns
- She has 7 fewer pinecones than acorns
- The meaning of 7 fewer pinecones than acorns is the number of the
pinecones is less than the number of acorns by 7
∵ She has 4 pinecones
∵ She has 7 fewer pinecones than acorns
- The number of pine cones is less than the number of acorns by 7
∴ 4 = number of acorns - 7
- Add 7 to both sides
∴ 11 = number of acorns
*<em> Lin has 11 acorns</em>
- Tom choose answer A which is 3
- He made a mistake in the equation
- He put ⇒ number of the acorns = 7 - 4 not 7 + 4
∴ number of acorns = 3
* <em>He subtract 4 from 7 instead of add 4 to 7</em>