Question

Derivada


Determine a derivada de f(x)= x²+3x+7 no ponto x0=0

Answer 1

$f(x)= x^2+3x+7\\ \\ f'(x)=2x+3\\ \\ f'(0)=2.0+3\\ \\ f'(0)=3$

Answer 2

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Derivada no ponto

$\Large\boxed{\boxed{\boxed{\boxed{\displaystyle\sf f'(a)=\lim_{ x \to a}\dfrac{f(x)-f(a)}{x-a}}}}}$

$\sf f(x)=x^2+3x+7\\\sf f(0)=0^2+3\cdot0+7=7\\\displaystyle\sf f'(0)=\lim_{x \to 0}\dfrac{x^2+3x+\diagup\!\!\!7-\diagup\!\!\!7}{x-0}\\\displaystyle\sf f'(0)=\lim_{ x \to 0}\dfrac{x^2+3x}{x}\\\displaystyle\sf f'(0)=\lim_{x \to 0}\dfrac{\diagdown\!\!\!x\cdot(x+3)}{\diagdown\!\!\!x}\\\displaystyle\sf f'(0)=\lim_{x \to 0}x+3=0+3\\\huge\boxed{\boxed{\boxed{\boxed{\sf f'(0)=3\checkmark}}}}$