(Solved):   Please answer correctly and neatly \[ f(x, y)=9-2 x^{2}-3 y^{2}, P(3,2) \] a. Find the grad ...

 

Please answer correctly and neatly

\[ f(x, y)=9-2 x^{2}-3 y^{2}, P(3,2) \] a. Find the gradient and evaluate it at \( P \). The gradient at \( P \) is \( \langle\square, \square \). (Type any angles in radians between 0 and \( 2 \pi \). Type an exact answer, using \( \pi \) as needed. Use a comma to separate answers as needed.) What angle(s) is/are associated with the direction of maximum decrease? (Type any angles in radians between 0 and \( 2 \pi \). Type an exact answer, using \( \pi \) as needed. Use a comma to separate answers as needed.) What angle(s) is/are associated with the direction of zero change? The angle(s) associated with the directions of zero change is/are (Type any angles in radians between 0 and \( 2 \pi \). Type an exact answer, using \( \pi \) as needed. Use a comma to separate answers as needed.) c. Write the directional derivative at \( P \) as a function of \( \theta \); call this function \( g(\theta) \). \( g(\theta)= \) d. Find the value of \( \theta \) that maximizes \( g(\theta) \) and find the maximum value. What value of \( \theta \) maximizes \( g(\theta) \) ? \( \theta= \) (Type any angles in radians between 0 and \( 2 \pi \). Type an exact answer, using \( \pi \) as needed.) What is the maximum value? \( \mathrm{g}(\theta)= \) (Type an exact answer, using radicals as needed.) Yes No