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If (x)= '(x) and (1)=2, then (3)=?

Question

If $\emptyset (x) = \emptyset^{'} (x)$ and $\emptyset (1) = 2,$ then $\emptyset (3) = ?$

e^{2}

2 e^{2}

3 e^{2}

2 e^{3}

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Evelyn Discussed

\emptyset (x) = \emptyset^{'} (x)

and

\emptyset (1) = 2,

then

\emptyset (3) = ?

14 mins ago

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14 mins ago

Text solutionVerified

In the above question it is given that

ϕ (x) = ϕ^{'} (x)

This condition is only followed by

ϕ (x) = a e^{x}

Given that

ϕ (1) = 2

\Rightarrow ϕ (1) = a e^{'}

\Rightarrow 2 = a e

\Rightarrow a = \frac{2}{e}

Therefore to find

ϕ (3)

put

x = 3

\Rightarrow ϕ (3) = a e^{3}

\Rightarrow ϕ (3) = \frac{2}{e} e^{3}

\Rightarrow ϕ (3) = 2 e^{2}

hence, (B) is the correct option.

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Question Text	If $\emptyset (x) = \emptyset^{'} (x)$ and $\emptyset (1) = 2,$ then $\emptyset (3) = ?$
Answer Type	Text solution:1
Upvotes	150