Question

Encontre o resultado de f’(x) e f’(2), quando:

Answer 1

a)

$\sf f(x)=3x-2\\\sf f'(x)=3\\\sf f'(2)=3$

b)

$\sf f(x)=\sqrt{x}\\\sf f'(x)=\dfrac{1}{2\sqrt{x}}\\\sf f'(2)=\dfrac{1}{2\sqrt{2}}=\dfrac{\sqrt{2}}{4}$

c)

$\sf f(x)=5x-1\\\sf f'(x)=5\\\sf f'(2)=5$

d)

$\sf f(x)=2x-5\\\sf f'(x)=2\\\sf f'(2)=2$

Answer 2

Oie, Td Bom?!

a) $f(x) = 3x - 2$

• $f'(x) = \frac{d}{dx} (3x - 2)$

$f'(x)= \frac{d}{dx} (3x) - \frac{d}{dx} (2)$

$f'(x)= 3 - 0$

$f'(x) = 3$

• $f'(2) = 3$

b) $f(x) = \sqrt{x}$

• $f'(x)= \frac{d}{dx} ( \sqrt{x} )$

$f'(x)= \frac{1}{2 \sqrt{x} }$

• $f'(2) = \frac{1}{2 \sqrt{2} }$

$f'(2) = \frac{1}{2 \sqrt{2} } \: . \: \frac{ \sqrt{2} }{ \sqrt{2} }$

$f'(2) = \frac{1 \sqrt{2} }{2 \sqrt{2} \sqrt{2} }$

$f'(2) = \frac{ \sqrt{2} }{2 \: . \: 2}$

$f'(2) = \frac{ \sqrt{2} }{4}$

c) $f(x) = 5x - 1$

• $f'(x) = \frac{d}{dx} (5x - 1)$

$f'(x) = \frac{d}{dx} (5x) - \frac{d}{dx} (1)$

$f'(x) = 5 - 0$

$f'(x) = 5$

• $f'(2) = 5$

d) $f(x) = 2x - 5$

• $f'(x) = \frac{d}{dx} (2x - 5)$

$f'(x) = \frac{d}{dx} (2x) - \frac{d}{dx} (5)$

$f'(x) = 2 - 0$

$f'(x) = 2$

• $f'(2) = 2$

Att. Makaveli1996