Find a First-Degree Polynomial Function P1 Whose Value and Slope $f$

question 63

Multiple Choice

Find a first-degree polynomial function P1 whose value and slope agree with the value and slope of $f$ at $x = c$ . What is $P _ { 1 }$ called?
$$f ( x ) = \frac { 4 } { \sqrt [ 3 ] { x } } , c = 27$$

• A) \(y = \frac { 4 } { 3 } + \frac { 4 } { 243 } ( x - 27 ) ;\) tangent line to \(y = f ( x )\) at \(x = 27\)
• B) \(y = \frac { 4 } { 3 } - \frac { 4 } { 243 } ( x - 27 )\); secant line to \(y = f ( x )\) at \(x = 27\)
• C) \(y = \frac { 4 } { 3 } + \frac { 4 } { 243 } ( x - 27 ) ;\) secant line to \(y = f ( x )\) at \(x = 27\)
• D) \(y = \frac { 4 } { 3 } + \frac { 4 } { 243 } ( x + 27 )\); secant line to \(y = f ( x )\) at \(x = 27\)
• E) \(y = \frac { 4 } { 3 } - \frac { 4 } { 243 } ( x - 27 )\); tangent line to \(y = f ( x )\) at \(x = 27\)

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