A scalar function is given by $f(x, y)=x^{2}+y^{2}$. Take $\hat{\imath}$ and $\hat{\jmath}$ as unit vectors along the $x$ and $y$ axes, respectively. At $(x, y)=(3,4),$ the direction along which $f$ increases the fastest is
(A) $\frac{1}{5}(4 \hat{\imath}-3 \hat{\jmath})$
(B) $\frac{1}{5}(3 \hat{\imath}-4 \hat{\jmath})$
(C) $\frac{1}{5}(3 \hat{\imath}+4 \hat{\jmath})$
(D) $\frac{1}{5}(4 \hat{\imath}+3 \hat{\jmath})$

Question ID - 155433 | SaraNextGen Top Answer

A scalar function is given by $f(x, y)=x^{2}+y^{2}$. Take $\hat{\imath}$ and $\hat{\jmath}$ as unit vectors along the $x$ and $y$ axes, respectively. At $(x, y)=(3,4),$ the direction along which $f$ increases the fastest is
(A) $\frac{1}{5}(4 \hat{\imath}-3 \hat{\jmath})$
(B) $\frac{1}{5}(3 \hat{\imath}-4 \hat{\jmath})$
(C) $\frac{1}{5}(3 \hat{\imath}+4 \hat{\jmath})$
(D) $\frac{1}{5}(4 \hat{\imath}+3 \hat{\jmath})$