1. Determina los intervalos sobre los cuales la gráfica es creciente o decreciente, los máximos y minimos, cóncava hacia arriba o hacia abajo y los puntos de inflexión. a. \( f(x)-x^{3}-6 x^{2}+12 x \) b. \( f(x)-2 x^{3}-3 x^{2}-12 x+5 \) c. \( f(x)-2 x^{4}-8 x+3 \) d. \( f(x)-x^{\prime}(x-4) \) e. \( f(x)=x(x-4)^{3} \)

Compute the work done by the force field \( F \) along the curve \( C \). \( \mathrm{F}(x, y)=\langle 2 x, 2 y\rangle, C \) is the line segment from \( (1,1) \) to \( (5,4) \) \( W=\square \)

Compute the work done by the force field \( F=\langle y, 0, z\rangle \) along the triangle from \( (0,0,0) \) to \( (2,3,4) \) then to \( (2,3,0) \) and then back to \( (0,0,0) \). \( W=\square \)

Compute the divergence of \( F(x, y)=1.2 x i+1.75 y j \) \( \operatorname{div} F=\square \)

Determine whether or not the vector field \( (x-46 x y) i+\left(y^{2}-23 x^{2}\right) j \) is conservative. If it is, find a potential function. \( f(x, y)=\frac{x^{2}}{2}-23 x^{2} y+y^{3}+c \). The field is not conservative. \( f(x, y)=x^{2}-23 x^{2} y+\frac{y^{3}}{3}+c \). The field is not conservative. \( f(x, y)=\frac{x^{2}}{2}-x^{2} y+\frac{y^{3}}{3}+c \). The field is conservative. \( f(x, y)=\frac{x^{2}}{2}-23 x^{2} y+\frac{y^{3}}{3}+c \). The field is conservative. \( f \)

\( \sum _ { y = 1 } ^ { n } \sum _ { x = 1 } ^ { n } 4 x + 7 y + x ^ { 2 } \)