The second derivative at the point (2,2) is 34/9
<u>Explanation:</u>
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2x⁴ = 4y³
2x⁴ - 4y³ = 0
We first need to find dy/dx and then d²y/dx²
On differentiating the equation in terms of x
dy/dx = d(2x⁴ - 4y³) / dx
We get,
dy/dx = 2x³/3y²
On differentiating dy/dx we get,
d²y/dx² = 2x²/y² + 8x⁶/9y⁵
d²y/dx² = 34/9
Therefore, the second derivative at the point (2,2) is 34/9
Answer:
Step-by-step explanation:
Isolate x on one side of the equation.
2(-2x-4) ← (Expand by using with distributive property.)
<u><em>DISTRIBUTIVE PROPERTY</em></u>
⇒ A(B+C)=AB+AC
⇒ A(B-C)=AB-AC
A=2
B=(-2x)
C=4
2(-2x)-2*4
-2*2x-2*4
-2*2x-2*4 (Solve.)
-2*2-2*4=-4x-8
Rewrite the equation problem.
10-x=-4x-8
10-x-10=-4x-8-10 (Subtract 10 from both sides.)
Solve.
-x=-4x-18
-x+4x=-4x-18+4x (Then, add 4x from both sides.)
3x=-18 (Solve.)
3x/3=-18/3 (Divide by 3 from both sides.)
-18/3 (Solve & Simplify.)
-18/3=-6
X=-6
Therefore, the correct answer is x=-6.
