At what points on the following curve, is the tangent parallel to x-axis ?
`y=x^(2)" on "[-2,2]`

Answer

To find the points on the curve \( y = x^2 \) where the tangent is parallel to the x-axis, we can follow these steps:

### Step 1: Understand the condition for the tangent to be parallel to the x-axis
A tangent line is parallel to the x-axis if its slope is zero. Therefore, we need to find where the derivative of the function is equal to zero.

### Step 2: Find the derivative of the function
The function given is:
\[ y = x^2 \]
To find the slope of the tangent, we differentiate \( y \) with respect to \( x \):
\[ \frac{dy}{dx} = 2x \]

### Step 3: Set the derivative equal to zero
To find the points where the tangent is parallel to the x-axis, we set the derivative equal to zero:
\[ 2x = 0 \]

### Step 4: Solve for \( x \)
Solving the equation \( 2x = 0 \) gives:
\[ x = 0 \]

### Step 5: Find the corresponding \( y \) value
Now we need to find the \( y \) value when \( x = 0 \):
\[ y = (0)^2 = 0 \]
Thus, the point is \( (0, 0) \).

### Step 6: Check if the point lies within the given interval
The point \( (0, 0) \) lies within the interval \([-2, 2]\).

### Conclusion
The point on the curve \( y = x^2 \) where the tangent is parallel to the x-axis is:
\[ (0, 0) \]