How do you graph #f(x)=6x15# using the information given by the first derivative?
graph{y=6x15 [40, 40, 20, 20]}
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To graph ( f(x) = 6x  15 ) using the information given by the first derivative, follow these steps:

Find the first derivative ( f'(x) ). ( f'(x) = \frac{d}{dx}(6x  15) ) ( f'(x) = 6 )

Determine the critical points by setting ( f'(x) ) to zero. ( 6 = 0 ) has no solution, so there are no critical points.

Identify the intervals where ( f'(x) ) is positive or negative. ( f'(x) = 6 ) is always positive.

Determine the behavior of ( f(x) ) in the intervals. Since ( f'(x) ) is always positive, ( f(x) ) is always increasing.

Sketch the graph:
 The graph of ( f(x) = 6x  15 ) is a straight line with a slope of 6 and a yintercept of 15.
 The graph is always increasing and has no turning points or inflection points.
Thus, the graph of ( f(x) = 6x  15 ) is a straight line that increases continuously without any critical points.
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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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