Question

Os pontos críticos de g(x)=|3x−4| é:

Answer 1

$\mathrm{g(x)=|3x-4|}\\\\ \mathrm{g'(x)=\frac{d}{dx}(|3x-4|)\ \to\ g'(x)=\dfrac{3x-4}{|3x-4|}\frac{d}{dx}(3x-4)}\\\\ \mathrm{g'(x)=\dfrac{3x-4}{|3x-4|}3\ \to\ \boxed{\mathrm{g'(x)=\dfrac{9x-12}{|3x-4|}}}}\\\\\\ \mathrm{\Rightarrow Pontos\ cr\'iticos\ \to\ \boxed{\mathrm{g'(x)=0}}}}\\\\\\ \mathrm{\dfrac{9x-12}{|3x-4|}=0\ \to\ 9x-12=0\ \to\ 9x=12}\\\\ \mathrm{x=\dfrac{12}{9}\ \to\ x=\dfrac{4}{3}\ \to\ \boxed{\boxed{\mathbf{x=1,\overline{3}}}}}$