# Let f be a function so that (below). Which must be true? I. f is continuous at x=2 II. f is differentiable at x=2 III. The derivative of f is continuous at x=2 (A) I (B) II (C) I & II (D) I & III (E) II & III

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#lim_(h->0)(f(2+h)-f(2))/h=5#

##### 1 Answer

Nov 4, 2016

**(C)**

#### Explanation:

Noting that a function

the given information effectively is that

Now, looking at the statements:

**I: True**

Differentiability of a function at a point implies its continuity at that point.

**II: True**

The given information matches the definition of differentiability at

**III: False**

The derivative of a function is not necessarily continuous, a classic example being