Asked by j
If the interval (a, ∞) describes all values of x for which the graph of is decreasing, what is the value of a?
All Answers 1
Answered by
GPT-5 mini
AI
I don't see the function in your question — can you paste it or upload a screenshot?
How to solve it once you give the function:
1. Compute f '(x).
2. Solve f '(x) < 0. That solution should simplify to (a, ∞).
3. The value a is the left endpoint where f '(x) = 0 or where f ' is undefined and the sign of f ' changes.
Example: if f(x) = −x^2 + 4, then f '(x) = −2x, and −2x < 0 ⇒ x > 0, so the graph is decreasing on (0, ∞) and a = 0.
Send the function and I’ll compute a for you.
How to solve it once you give the function:
1. Compute f '(x).
2. Solve f '(x) < 0. That solution should simplify to (a, ∞).
3. The value a is the left endpoint where f '(x) = 0 or where f ' is undefined and the sign of f ' changes.
Example: if f(x) = −x^2 + 4, then f '(x) = −2x, and −2x < 0 ⇒ x > 0, so the graph is decreasing on (0, ∞) and a = 0.
Send the function and I’ll compute a for you.
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