Question

8. If f(x) = f'(x) and f(1) = 2, then f(3) equals
(a) e
(b) 2e2
(c) 3e2
(d) none of t
12..​

Answer 1

Answer:

GIVEN THAT :‐

f(x) = f'(x)

SUPPOSE f(x) = y then –

$y = \frac{dy}{dx}$

$\frac{dy}{y} = dx$

Integrate both side –

$log(y) = x + c$

if x = 1 , y = 2 then –

$c = log(2) - 1$

So ,

$log(y) = x + log(2) - 1$

When x = 3 the y is –

$log(y) = 2 + log(2)$

$y = {e}^{2 + log(2) } \\ \\ y = {e}^{2} .2 \\ \\ y = 2 {e}^{2}$

So, f(3) = 2 e².

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