(b) You start to move in the direction you found in part (a) at a speed of 3 cm/sec. How fast is the concentration changing

Complete Question

The concentration of salt in a fluid at (x,y,z) is given by F(x,y,z)=x^2+y^4+2x^2z^2 mg/cm3 You are at the point (1,1,1).

a. In which direction should you move if you want the concentration to increase the fastest?

I keep getting <5,2,8> for this answer and it says it is incorrect

You start to move in the direction you found in part (a) at a speed of 4 cm/sec. How fast is the concentration changing?

a

b

Explanation:

From the question we are told that

  The equation is

differentiating with respect to x

differentiating with respect to y

differentiating with respect to z

Gnerally the rate of change of the salt concentration is mathematically represented as

=>  

At  the point (1,1,1)

=>

generally rate at which the concentration is changing is mathematically represented as

=>      

=>    

=>    

=>    

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find the sum of the two horizontal vectors and the sum of the two vertical vectors

isoceles right angled triangle