Answer:
39/16
Step-by-step explanation:
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: 8y^6x^6
Step-by-step explanation:
Volume = l*w*h so multiply all the variable by <u>multiplying the numbers and adding the exponents</u> so
2y^2*4x^4y=8y^3x^4
then 8y^3x^4*x^2y^3=8y^6x^6
Answer:
614656h²⁸k⁸
Step-by-step explanation:
Exponent Power Rule:
Step 1: Write expression
[4h⁷7k²]⁴
Step 2: Distribute power 4 to each term
4⁴h⁷⁽⁴⁾7⁴k²⁽⁴⁾
Step 3: Simplify
256h⁷⁽⁴⁾2401k²⁽⁴⁾
614656h⁷⁽⁴⁾k²⁽⁴⁾
Step 4: Use Exponent Rule
614656h²⁸k⁸