Question

The graph of y = f(x) contains the point (0,2), \frac{dy}{dx}=\frac{-x}{ye^{x^2}}, and f(x) is greater than 0 for all x, then f(x)= A) 3+e^{-x^2} B) \sqrt{3}+e^{-x} C) 1+e^{-x} D) \sqrt{3+e^{-x^2}} E) \sqrt{3+e^{x^2}}

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ANSWERED
asked 2021-03-20
The graph of y = f(x) contains the point (0,2), \(\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={\frac{{-{x}}}{{{y}{e}^{{{x}^{{2}}}}}}}\), and f(x) is greater than 0 for all x, then f(x)=
A) \(\displaystyle{3}+{e}^{{-{x}^{{2}}}}\)
B) \(\displaystyle\sqrt{{{3}}}+{e}^{{-{x}}}\)
C) \(\displaystyle{1}+{e}^{{-{x}}}\)
D) \(\displaystyle\sqrt{{{3}+{e}^{{-{x}^{{2}}}}}}\)
E) \(\displaystyle\sqrt{{{3}+{e}^{{{x}^{{2}}}}}}\)

Answers (1)

2021-03-22
Answer B)
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