Let f be a function of two variables that has continuous partial derivatives and consider the points a(7, 3), b(12, 3), c(7, 7), and d(15, 9). the directional derivative of f at a in the direction of the vector ab is 5 and the directional derivative at a in the direction of ac is 4. find the directional derivative of f at a in the direction of the vector ad. (round your answer to two decimal places.)
Accepted Solution
A:
The directional derivative of a function [tex]f(x,y)[/tex] in the direction of [tex]\mathbf v[/tex] is given by
[tex]\nabla f(x,y)\cdot\mathbf v[/tex]
We have [tex]\vec{ab}=\mathbf b-\mathbf a=(12-7,3-3)=(5,0)[/tex], so that [tex]\|\vec{ab}\|=5[/tex], at which point we're given