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Which one of these functions is decreasing for all real values of x? Circle your answer - AQA - A-Level Maths: Pure - Question 1 - 2020 - Paper 2
Question 1
Which one of these functions is decreasing for all real values of x? Circle your answer. f(x) = e^x f(x) = -e^{1-x} f(x) = -e^{x-1} f(x) = -e^{-x}
Worked Solution & Example Answer:Which one of these functions is decreasing for all real values of x? Circle your answer - AQA - A-Level Maths: Pure - Question 1 - 2020 - Paper 2
Step 1
Identify which function is decreasing
Answer
To determine which function is decreasing for all real values of , we can analyze the derivatives of the given functions:
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For , the derivative is , which is always positive. Thus, this function is increasing.
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For , the derivative is: This is also always positive, indicating the function is increasing.
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For , the derivative is: This is always negative, indicating that this function is decreasing.
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For , the derivative is: This is also positive, indicating that this function is increasing.
Based on the analysis, the function that is decreasing for all real values of is:
.