Question

Dada a função qual o valor de f ' (1) ? Escolha uma: a. 2 b. - 5/4 c. 2/5 d. 3/2 e. 1

Answer 1

Regra do quociente:

$f(x)=\dfrac{u(x)}{v(x)}\to f'(x)=\dfrac{u'(x)v(x)-u(x)v'(x)}{v^2(x)}$

Logo:

$u(x)=3x^2-4x+2\to u'(x)=6x-4\\\\v(x)=x-3\to v'(x)=1\\\\\\f'(x)=\dfrac{(6x-4)(x-3)-(3x^2-4x+2)}{(x-3)^2}\\\\\\f'(1)=\dfrac{(6(1)-4)((1)-3)-(3(1)^2-4(1)+2)}{((1)-3)^2}=\dfrac{(2)(-2)-(1)}{(-2)^2}=\boxed{-\dfrac54}$