# I think the correct answer is the ONLY first one. Am I right?

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Which of the following properties are satisfied by the function

#f(x)=#

#x^2+1∣x<0#

#1∣x=0#

#5x+1∣x>0#

(I) f(x) is continuous

(II) f(x) is differentiable for all x

(III) f(x) is differentiable at x = -2

Which of the following properties are satisfied by the function

(I) f(x) is continuous

(II) f(x) is differentiable for all x

(III) f(x) is differentiable at x = -2

##### 1 Answer

The correct answers are the first and the third.

#### Explanation:

**First Answer**

The function is indeed continuous. In fact, it is composed by three continuous patched, which connect continously at

**Second Answer**

The function is not differentiable everywhere: the derivative for negative

**Third answer**

The function is differentiable at