Siendo 1/(3x^2), ¿cuál es la ecuación de la recta perpendicular a f(x) que pasa por el vértice de la función 2(4x^3 - x^2)? a) 3x + 2 b) 2x - 3 c...

Para encontrar a equação da reta perpendicular à função f(x) e que passa pelo vértice da função g(x), podemos seguir os seguintes passos: 1. Encontre a derivada da função f(x) para determinar a inclinação da reta tangente à curva no ponto desejado. 2. Determine a inclinação da reta perpendicular à reta tangente encontrada no passo anterior. A inclinação da reta perpendicular é o inverso negativo da inclinação da reta tangente. 3. Utilize a fórmula da reta (y = mx + b) e substitua a inclinação encontrada no passo anterior e as coordenadas do ponto desejado para encontrar o valor de b, que é o coeficiente linear da reta. No caso da função f(x) = 1/(3x^2) e da função g(x) = 2(4x^3 - x^2), vamos seguir esses passos: 1. Derivando a função f(x), temos: f'(x) = -2/(3x^3) 2. A inclinação da reta perpendicular à reta tangente é o inverso negativo da inclinação da reta tangente. Portanto, a inclinação da reta perpendicular é: m = -1/f'(x) = -1/(-2/(3x^3)) = 3x^3/2 3. Agora, vamos encontrar o vértice da função g(x) = 2(4x^3 - x^2). Para isso, igualamos a derivada de g(x) a zero e resolvemos para x: g'(x) = 0 24x^2 - 2x = 0 2x(12x - 1) = 0 x = 0 ou x = 1/12 Substituindo x = 1/12 na função g(x), encontramos o valor de y: g(1/12) = 2(4(1/12)^3 - (1/12)^2) = 2(1/432 - 1/144) = 2/432 = 1/216 Portanto, o ponto do vértice é (1/12, 1/216). Agora, podemos utilizar a fórmula da reta (y = mx + b) e substituir a inclinação m = 3x^3/2 e as coordenadas do ponto (1/12, 1/216) para encontrar o valor de b: 1/216 = (3(1/12)^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12) + b 1/216 = (3/12^3/2)(1/12)