Question

A diferença de f’(2) menos g’(3) será dada por:

Answer 1

Derivando f(x) e encontrando f'(2):

$f'(x) = 24x + 0{,}55.2.e^{2x} - \frac{1}{x} \Rightarrow f'(x) = 24x -\frac{1}{x} + 1{,}1.e^{2x}\\\\\textsf{Para f'(2):} ~~f'(2) = 24.2 - \frac{1}{2} + 1{,}1.e^{2.2} = 47{,}5 + 1{,}1.e^{4} \approx 107{,}56$

Derivando g(x) e encontrando g'(3):

$g'(x) = \frac{1}{2}.(-2).\frac{1}{x^3} + 0{,}75.0{,}5\frac{1}{\sqrt{x}} - (-0{,}3).e^{-0{,}3x}\\\\g'(x) = \frac{-1}{x^3} + \frac{0{,}375}{\sqrt{x}} + 0{,}3.e^{-0{,}3x}\\\\\textsf{Para g'(3):}~~g'(3)=\frac{-1}{3^3} + \frac{0{,}375}{\sqrt{3}} + 0{,}3.e^{-0{,}3.3} \approx 0{,}30 }$

Portanto, a diferença de f'(2) e g'(3) será, aproximadamente:

$107{,}56-0{,}30 = \boxed{107{,}26}$