considerando o grafico da função abaixo,
Anexos:
Soluções para a tarefa
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Boa tarde João!
Solução!
Para encontramos a equação tangente,vamos derivar a função e em seguida substituir o valor de x,para encontramos o coeficiente angular m da reta.
![y= x^{3}-3 x^{2} -x+5\\\\\\
y'=3 x^{2} -6x-1\\\\\\
m= 3 x^{2} -6x-1\\\\\\
Q(3,2)\\\\\\
Substituindo!\\\\\\\
m= 3 (3)^{2} -6(3)-1\\\\\\
m=3.(9)-6(3)-1\\\\\\
m=27-18-1\\\\\
m=27-19\\\\\\
\boxed{m=8}](https://tex.z-dn.net/?f=y%3D+x%5E%7B3%7D-3+x%5E%7B2%7D+-x%2B5%5C%5C%5C%5C%5C%5C%0Ay%27%3D3+x%5E%7B2%7D+-6x-1%5C%5C%5C%5C%5C%5C%0Am%3D+3+x%5E%7B2%7D+-6x-1%5C%5C%5C%5C%5C%5C%0AQ%283%2C2%29%5C%5C%5C%5C%5C%5C%0ASubstituindo%21%5C%5C%5C%5C%5C%5C%5C%0Am%3D+3+%283%29%5E%7B2%7D+-6%283%29-1%5C%5C%5C%5C%5C%5C%0Am%3D3.%289%29-6%283%29-1%5C%5C%5C%5C%5C%5C%0Am%3D27-18-1%5C%5C%5C%5C%5C%0Am%3D27-19%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7Bm%3D8%7D "y= x^{3}-3 x^{2} -x+5\\\\\\
y'=3 x^{2} -6x-1\\\\\\
m= 3 x^{2} -6x-1\\\\\\
Q(3,2)\\\\\\
Substituindo!\\\\\\\
m= 3 (3)^{2} -6(3)-1\\\\\\
m=3.(9)-6(3)-1\\\\\\
m=27-18-1\\\\\
m=27-19\\\\\\
\boxed{m=8}")
Equação da reta!
![Q(3,2)\\\\\\
m=8\\\\\\\
y-yQ=m(x-xQ)\\\\\\
y-2=8(x-3)\\\\\\
y-2=8x-24\\\\\\
y=8x-24+2\\\\\\
y=8x-22\\\\\
y-8x+22=0\\\\\\\\\\\
\boxed{Resposta:y-8x+22=0~~\boxed{Alternativa~~C}}](https://tex.z-dn.net/?f=Q%283%2C2%29%5C%5C%5C%5C%5C%5C%0Am%3D8%5C%5C%5C%5C%5C%5C%5C%0A%0A%0Ay-yQ%3Dm%28x-xQ%29%5C%5C%5C%5C%5C%5C%0Ay-2%3D8%28x-3%29%5C%5C%5C%5C%5C%5C%0Ay-2%3D8x-24%5C%5C%5C%5C%5C%5C%0Ay%3D8x-24%2B2%5C%5C%5C%5C%5C%5C%0Ay%3D8x-22%5C%5C%5C%5C%5C%0Ay-8x%2B22%3D0%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7BResposta%3Ay-8x%2B22%3D0%7E%7E%5Cboxed%7BAlternativa%7E%7EC%7D%7D "Q(3,2)\\\\\\
m=8\\\\\\\
y-yQ=m(x-xQ)\\\\\\
y-2=8(x-3)\\\\\\
y-2=8x-24\\\\\\
y=8x-24+2\\\\\\
y=8x-22\\\\\
y-8x+22=0\\\\\\\\\\\
\boxed{Resposta:y-8x+22=0~~\boxed{Alternativa~~C}}")
Boa tarde!
Bons estudos!
Solução!
Para encontramos a equação tangente,vamos derivar a função e em seguida substituir o valor de x,para encontramos o coeficiente angular m da reta.
Equação da reta!
Boa tarde!
Bons estudos!
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