Answer:
The volume of fish tank is
Step-by-step explanation:
Area of Base of fish tank =
We are given that A fish tank has a base, B, with an area, in square inches, modeled by
So,
Height of tank = x+3
Volume of tank =
So, Volume of tank =
Volume of Tank =
Hence The volume of fish tank is
The critical points of <em>h(x,y)</em> occur wherever its partial derivatives and
vanish simultaneously. We have
Substitute <em>y</em> in the second equation and solve for <em>x</em>, then for <em>y</em> :
This is to say there are two critical points,
To classify these critical points, we carry out the second partial derivative test. <em>h(x,y)</em> has Hessian
whose determinant is . Now,
• if the Hessian determinant is negative at a given critical point, then you have a saddle point
• if both the determinant and are positive at the point, then it's a local minimum
• if the determinant is positive and is negative, then it's a local maximum
• otherwise the test fails
We have
while
So, we end up with
Answer:
y=tanx+C
Step-by-step explanation:
