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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
the units of measurement for the composite function s(w(h)) is . Correct option A) .
<u>Step-by-step explanation:</u>
Here we have , Mary paints wooden signs and sells them at craft fairs. The function s(t) approximates how many signs Mary paints per hour. The function w(h) represents how many hours per week Mary spends painting the wooden signs. We need to find What are the units of measurement for the composite function s(w(h)) . Let's find out:
Basically we have two functions as ,
s(t) : how many signs Mary paints per hour
⇒
w(h) : how many hours per week Mary spends painting the wooden signs
⇒
In function composition, if we have two function f(x) and g(x) then
(f.g)(x) or f(g(x)) means first apply g(), then apply f() i.e. applying function f to the results of function g. So , In s(w(h)) :
⇒
⇒
Therefore , the units of measurement for the composite function s(w(h)) is . Correct option A) .