Write the Function in the Form Y = F(u) and U

question 272

Multiple Choice

Write the function in the form y = f(u) and u = g(x) . Then find dy/dx as a function of x.
- $$y = ( - 2 x + 11 ) ^ { 5 }$$

• A) \(y = u ^ { 5 } ; u = - 2 x + 11 ; \frac { d y } { d x } = - 10 ( - 2 x + 11 ) ^ { 4 }\)
• B) \(y = 5 u + 11 ; u = x ^ { 5 } ; \frac { d y } { d x } = - 10 x ^ { 4 }\)
• C) \(y = u ^ { 5 } ; u = - 2 x + 11 ; \frac { d y } { d x } = - 2 ( - 2 x + 11 ) ^ { 5 }\)
• D) \(y = u ^ { 5 } ; u = - 2 x + 11 ; \frac { d y } { d x } = 5 ( - 2 x + 11 ) ^ { 4 }\)

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Definitions:

Regressive

A term usually used to describe a tax system in which the tax rate decreases as the taxable amount increases, effectively placing a higher burden on lower-income earners.

Indirect

Pertains to actions, effects, or financial transactions that are not direct or straightforward, often referring to indirect taxes or costs.

Direct

A straightforward approach or method that does not involve intermediaries or detours.

Public Goods

Goods or services produced by the government; they can be jointly consumed by many individuals simultaneously at no additional cost and with no reduction in quality or quantity.