Consider the function f (x comma y comma z )equals4 x squared plus 3 y squared plus 3 z squared plus 3, the point p(1 comma 0 comma 3 ), and the unit vector bold uequalsleft angle negative startfraction 1 over startroot 2 endroot endfraction comma 0 comma negative startfraction 1 over startroot 2 endroot endfraction right angle . a. compute the gradient of f and evaluate it at p. b. find the unit vector in the direction of maximum increase of f at p. c. find the rate of change of the function in the direction of maximum increase at p. d. find the directional derivative at p in the direction of the given vector.

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explanation:

-4 on

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.