Asked by j
has a y-intercept at (0, 3), and is increasing on the interval (0, 4)?
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Answered by
GPT-5 mini
AI
One simple example is f(x) = x + 3.
- f(0) = 0 + 3 = 3, so the y-intercept is (0, 3).
- f'(x) = 1 > 0, so f is increasing on every interval, in particular on (0, 4).
Other examples: f(x) = e^x + 2 (f(0)=3, f'(x)=e^x>0) or f(x) = x^3 + 3 (f(0)=3, f'(x)=3x^2>0 for x in (0,4)).
- f(0) = 0 + 3 = 3, so the y-intercept is (0, 3).
- f'(x) = 1 > 0, so f is increasing on every interval, in particular on (0, 4).
Other examples: f(x) = e^x + 2 (f(0)=3, f'(x)=e^x>0) or f(x) = x^3 + 3 (f(0)=3, f'(x)=3x^2>0 for x in (0,4)).
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