Find a Function F(x) with the Following Property: F'(x) = $\mathrm { e } ^ { 2 x }$

question 37

Multiple Choice

Find a function f(x) with the following property: f'(x) = 2 $\mathrm { e } ^ { 2 x }$ - $\frac {4} { \mathrm { x }}$ + $\frac { 3 } { x ^ { 2 } }$ , f(1) = -2.

• A) f(x) = \(\mathrm { e } ^ { 2 x }\) - 4 ln|x| - \(\frac { 3 } { x }\) - ( \(e ^ { 2 }\) - 1)
• B) f(x) = \(\mathrm { e } ^ { 2 x }\) - 4 ln|x| - \(\frac { 6 x } { x ^ { 3 } }\) + 3 + 4e
• C) f(x) = \(\frac { 2 } { 3 }\) \(e ^ { 3 x }\) - 4x - \(\frac { 1 } { x }\) + \(\frac { 5 } { 3 }\)
• D) f(x) = \(\frac { 2 } { 3 }\) \(e ^ { 3 x }\) - 4 ln|x| - \(\frac { 1 } { x }\) - \(\frac { 5 } { 3 }\)

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