Question

Dada a função f(x)=√x.g(x),onde g(4)=2 e g(4)=3, o valor de f(4)é

Answer 1

Queremos f '(4) e Temos as informações :

$\text{f(x)} = \sqrt{\text x}.\text {g(x) }$

$\text{g(4)} = 2$

$\text{g '(4)} = 3$

Derivando a f(x) :

$\text{f '(x)} = (\sqrt{\text x})'.\text {g(x) }+\sqrt{\text x}.\text{g '(x) }$

$\displaystyle \text{f '(x)} = \frac{1}{2\sqrt{\text x}}.\text {g(x) }+\sqrt{\text x}.\ \text{g '(x) }$

fazendo x = 4 :

$\displaystyle \text{f '(4)} = \frac{1}{2\sqrt{4}}.\text {g(4) }+\sqrt{4}.\ \text{g '(4) }$

$\displaystyle \text{f '(4)} = \frac{1}{2.2}.2+2.3$

$\displaystyle \text{f '(4)} = \frac{1}{2}+6$

$\displaystyle \text{f '(4)} = \frac{13}{2}$

$\huge\boxed{\displaystyle \text{f '(4)} = 6,5}\checkmark$

Letra c