Question

sendo $f(x)= \sqrt[3] x^{2}+x+1$ , a derivada de f¹(-1) vale:

a)-1/3
b)1/2
c)1/3
d)-1
e)-1/2

Answer 1

f(x)=x^(2/3)+x+1
$f'(x)= \frac{2}{3}. x^{ \frac{2}{3}-1 } +x'+1' \\ f'(x)= \frac{2}{3}. x^{ \frac{-1}{3} } +1 \\ f'(-1)=\frac{2}{3}. (-1)^{ \frac{-1}{3} } +1 \\ F'(x)=-\frac{2 }{3} } +1 \\ F'(x)=\frac{1 }{3} }$

c