Find polynomial $g(x,y,t)$ with degree up to 2 such that the directional derivate of $f(x,y) = \int _{-6}^4g\left(x,y,t\right)dt\ $ at the point $(3,8)$ in the direction $-6\hat{i}+7\hat{j}$ equals $-8$
I really don't know how to find such polynomial, the only thing I did is to normalize the direction vector to be unit vector but how you manage to find such polynomial that satisfy it? I didn't learn how to calculate gradient for such functions