How do you find stationary and inflection points for #x^22x3#?
The unique stationary point is
When the derivative is zero at a point, it is referred to as "stationary"; these points are also known as critical points and are typically local extreme or "turning" points, though they are not always.
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To find stationary points, you need to find the critical points by taking the derivative of the function and setting it equal to zero. Then solve for ( x ).
Given the function ( f(x) = x^2  2x  3 ):

Find the derivative ( f'(x) ). [ f'(x) = 2x  2 ]

Set ( f'(x) ) equal to zero and solve for ( x ). [ 2x  2 = 0 ] [ 2x = 2 ] [ x = 1 ]
So, ( x = 1 ) is a critical point.
To determine if it's a maximum, minimum, or neither, you can use the second derivative test. If ( f''(x) > 0 ), it's a minimum; if ( f''(x) < 0 ), it's a maximum. If ( f''(x) = 0 ), the test is inconclusive.
 Find the second derivative ( f''(x) ). [ f''(x) = 2 ]
Since ( f''(x) ) is positive for all ( x ), the critical point ( x = 1 ) corresponds to a minimum.
Now, to find the inflection point(s), you need to find where the concavity changes, which occurs where the second derivative ( f''(x) ) equals zero or is undefined. Since ( f''(x) ) is a constant function in this case, there are no inflection points for ( f(x) = x^2  2x  3 ).
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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