True or False ExerciseIndicate whether the following statements are true or false.a. Suppose the function f(x,y) has a gradient gradf at(a,b). Then the vector (:fx,fy,-1:)is perpendicular to the the surface f(x,y)=zat(a,b,f(a,b))b. Suppose f(x,y)=2x2+3y2. Then 0Duf(1,0)4c. Suppose f(x,y)=y2x. Then the surface contains the curve (:t,t2,t3:).d. Suppose fis differentiable at(a,b) and gradf(a,b)=(0,0). Then f has a local maximum or minimum at(a,b)e. Suppose lim(x,y)(0,0)f(x,y)=4 along the x-axis, y-axis, and the line y=-3x and f(0,0)=4. Then f must be continuous at(0,0).f. Suppose f:R2Risan arbitrary function whose first and second partial derivatives exist. Then fxy=fyx.g. Suppose the contours of a continuous function f(x,y) are all parallel lines, then the graph of the function fis a plane.