The contrapositive of statement:
If f(x) is continuous at x=a then f(x) is differentiable at x=a

Options

A. If `f(x)` is continuous at x=a then `f(x)` is not continuous at x=a
B. If `f(x)` is not differentiable at x=a then `f(x)` is not continuous at x=a
C. If `f(x)` is differentiable at x=a then `f(x)` is continuous at x=a
D. If `f(x)` is differentiable at x=a then `f(x)` is not continuous

Answer

To find the contrapositive of the statement "If f(x) is continuous at x=a, then f(x) is differentiable at x=a," we can follow these steps:

### Step 1: Identify the original statement
The original statement can be expressed in the form of an implication:
- Let \( p \): "f(x) is continuous at x=a"
- Let \( q \): "f(x) is differentiable at x=a"

Thus, the statement is:
\[ p \implies q \]

### Step 2: Write the contrapositive
The contrapositive of an implication \( p \implies q \) is given by:
\[ \neg q \implies \neg p \]
where \( \neg q \) is the negation of \( q \) and \( \neg p \) is the negation of \( p \).

### Step 3: Determine the negations
- The negation of \( q \) (f(x) is differentiable at x=a) is:
\[ \neg q: \text{f(x) is not differentiable at x=a} \]

- The negation of \( p \) (f(x) is continuous at x=a) is:
\[ \neg p: \text{f(x) is not continuous at x=a} \]

### Step 4: Formulate the contrapositive statement
Now substituting the negations into the contrapositive form:
\[ \neg q \implies \neg p \]
This translates to:
"If f(x) is not differentiable at x=a, then f(x) is not continuous at x=a."

### Final Answer
Thus, the contrapositive of the given statement is:
**If f(x) is not differentiable at x=a, then f(x) is not continuous at x=a.**