Calculate the directional derivative of f in the direction

Question

Let f(x, y. z) = x² + xy + yz.

a. Calculate Delta (f)(l. 2,5).

b. Calculate the directional derivative of f in the direction of <1, -2, 3> at the point (1, 2, 5) (In notation: D_v(f)(1, 2, 5)).

c. Find a vector v such that D_v(f)(1, 2, 5) = 0.

d. Find a vector w such that d_c(f)(1, 2, 5) has largest value. what is this largest w?

e. Find a vector p such that D_p(f)(1, 2, 5) has smallest value. What is this smallest w?