Question

Derivada da função f(x)=x^3-5x^2, no ponto x0=5

Answer 1

f(x) = x³ - 5 x²

f'(x) = 3 x² - 10 x

f'(5) = 3 . 25 - 50

f'(5) = 25

Answer 2

Derivada no ponto

$\large \: f'(a)=\mathsf{\lim_{x \to a}\dfrac{f(x)-f(a)}{x-a}}$

$\mathsf{f'(5)=\lim_{x \to 5}\dfrac{{x}^{3}-5{x}^{2}-0}{x-5}}$

$\mathsf{f'(5)=\lim_{x \to 5}\dfrac{{x}^{2}\cancel{(x-5)}}{\cancel{(x-5)}}}$

$\mathsf{f'(5)=\lim_{x \to 5}{x}^{2}={5}^{2}=25}$

$\large\boxed{\boxed{\mathsf{f'(5)=\lim_{x \to 5}\dfrac{{x}^{3}-5{x}^{2}}{x-5}=25}}}$