How do you sketch the graph that satisfies f'(x)>0 when x does not equal 2, f(2)=1?
I would apologize for being pedantic, but this is an educational website.
So,
graph{y1=3(x2) [1.907, 9.19, 2.45, 3.1]}
graph{e^(x2) [1.29, 8.574, 2.14, 2.793]}
Or
graph{(x2)^(1/3)+1 [2.68, 5.113, 0.86, 3.037]}
(3) Or we could have a translation of an odd power function.
graph{(x2)^(7/3)+1 [1.216, 3.65, 0.128, 2.305]}
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Since the derivative is greater than
A perfect example of this would be the cubic function
Hopefully this helps!
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To sketch the graph of a function ( f(x) ) such that ( f'(x) > 0 ) when ( x \neq 2 ) and ( f(2) = 1 ), we follow these steps:

Determine the behavior of the function around ( x = 2 ):
 Since ( f'(x) > 0 ) when ( x \neq 2 ), it implies that the function is increasing for all ( x ) values except at ( x = 2 ).
 At ( x = 2 ), ( f(2) = 1 ), which means there is a point on the graph at ( (2, 1) ).

Sketch the graph:
 Draw an increasing curve that passes through the point ( (2, 1) ).
 The curve should approach but not touch the point ( (2, 1) ) from both sides.
 Ensure that the curve is strictly increasing for ( x \neq 2 ).

Label the graph appropriately:
 Label the point ( (2, 1) ) to indicate the specific value of the function at ( x = 2 ).
 Optionally, include arrows or annotations to indicate the direction of the curve and the behavior of the function around ( x = 2 ).

Check the graph:
 Ensure that the graph satisfies the conditions given: ( f'(x) > 0 ) for ( x \neq 2 ) and ( f(2) = 1 ).
 Verify that the graph represents an increasing function for ( x \neq 2 ) and includes the specified point at ( (2, 1) ).
By following these steps, you can sketch the graph of the function that satisfies the given conditions.
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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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