Expand the Expression in the Difference Quotient and Simplify $\frac { f ( x + h ) - f ( x ) } { h }$

question 128

Multiple Choice

Expand the expression in the difference quotient and simplify. $\frac { f ( x + h ) - f ( x ) } { h }$ Difference quotient $f ( x ) = ( x ) ^ { 3 }$

• A) \(\frac { 3 x ^ { 2 } + 3 x h + h ^ { 2 } } { h }\)
• B) \(3 x ^ { 2 } - 3 x h - h ^ { 2 }\)
• C) \(\frac { 3 x ^ { 2 } + 3 x h - h ^ { 2 } } { h }\)
• D) \(3 x ^ { 2 } + 3 x h - h ^ { 2 }\)
• E) \(3 x ^ { 2 } + 3 x h + h ^ { 2 }\)

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Definitions:

Bone Marking

Features on the surface of bones, such as ridges and notches, which serve as attachment points for muscles and ligaments.

Foramen

An opening, hole, or passage, often in bone, through which nerves or blood vessels may pass.

Diploë

Diploë refers to the spongy bone layer between the inner and outer layers of cortical bone in the skull, which houses marrow and blood vessels.

Spongy Bone

A type of bone that is porous and less dense, found at the ends of long bones and in the inner layers of other bones, providing structural support and flexibility.