Find All Possible Functions with the Given Derivative $y ^ { \prime } = 4 x ^ { 2 } + 1$

question 246

Multiple Choice

Find all possible functions with the given derivative.
- $y ^ { \prime } = 4 x ^ { 2 } + 1$

• A) \(x + C\)
• B) \(\frac { 4 } { 3 } x ^ { 3 } + C\)
• C) \(\frac { 4 } { 3 } x ^ { 3 } + x + C\)
• D) \(8 x + C\)

---

Definitions:

Double-Declining-Balance

A method of accelerated depreciation which doubles the regular depreciation rate, reducing the value of an asset more quickly in its early years.

Scrap Value

The estimated value that an asset will realize upon its sale at the end of its useful life, typically a minimal amount reflecting its residual value.

Straight-Line Method

A depreciation method that allocates an equal amount of the cost of an asset to each year of its useful life.

Scrap Value

The projected amount an asset is expected to generate when it is sold after reaching the end of its lifespan.