If f(x) = 3x^2 + 3 then for which value of x, f’(x) = f(x)? - Vidyadip

Question

If $f(x) = 3x^2 + 3$ then for which value of $x, f’(x) = f(x)?$

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Answer

Here, $f(x) = 3x^2 + 3$

$\therefore f'(x) = 6x + 0 = 6x$

Now, $f’(x) = f(x)$

$6x = 3x^2 + 3$

$\therefore 3x^2 – 6x + 3 = 0$

$\therefore x^2 – 2x + 1 = 0$

$\therefore (x - 1)^2 = 0$

$\therefore (x - 1) (x - 1) = 0$

$\therefore x = 1$

Hence, if $x = 1$, then $f’(x) = f(x).$

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