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Over which interval of the domain is the function increasing?

A. (-[infinity], 4)
B. (1, 4)
C. (-[infinity] , 4)
D. (-[infinity] ,1)

1 Answer

5 votes

Final Answer:

The derivative of the function is e^x. Since e^x is always positive, the function is increasing over the entire interval of its domain, which is (-∞, ∞). None of the given options is answer.

Step-by-step explanation:

The derivative of the function is e^x, which is always positive.

Steps to solve:

Take the derivative of the function:

d/dx(e^x+1) = d/dx(e^x) + d/dx(1)

= e^x + 0

= e^x

Analyze the derivative:

e^x > 0

for all x ∈ (-∞, ∞)

Conclusion:

Since the derivative is always positive, the function is increasing over the entire interval of its domain, which is (-∞, ∞).

None of the given options is answer.

User Gilles Gregoire
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