If-f-x-3-x-2-find-f-3-h-f-3-h-

Question Number 181014 by Mastermind last updated on 20/Nov/22

If f (x) = 3 - x^{2}, find \frac{f (3 + h) - f (3)}{h}

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Commented by CElcedricjunior last updated on 20/Nov/22

f (x) = 3 - x^{2}

\lim_{h \to 0} \frac{f (3 + h) - f (3)}{h} = \lim_{h \to 0} \frac{3 - 9 - 6 h - h^{2} - 6}{h}

= \lim_{h \to 0} \frac{- (12 + 6 h + h^{2})}{h} = \frac{- 12}{0^{\mp}} = {\begin{cases} + \infty s i 0^{-} \\ - \infty s i 0^{+} \end{cases}

Commented by mr W last updated on 20/Nov/22

m a y b e y o u w a n t t o a s k

find \lim_{h \to 0} \frac{f (3 + h) - f (3)}{h} ?

Commented by Mastermind last updated on 20/Nov/22

i think it should be like that

Commented by mr W last updated on 20/Nov/22

t h i s i s y o u r q u e s t i o n . y o u s h o u l d k n o w

w h a t y o u w a n t t o a s k, o r n o t ?

Commented by Frix last updated on 20/Nov/22

\frac{f (3 + h) - f (3)}{h} = \frac{3 - {(3 + h)}^{2} - (3 - 3^{2})}{h} =

= \frac{3 - 9 - 6 h - h^{2} - 3 + 9}{h} = - \frac{6 h + h^{2}}{h} = - 6 - h

\Rightarrow

\lim_{h \to 0} \frac{f (3 + h) - f (3)}{h} = f^{'} (3) = - 6 as it should be

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