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

question 15

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?
$$f ( x ) = \tan x , c = - \frac { \pi } { 6 }$$

• A)
• \(3 y + \sqrt { 3 } = - 4 \left( x + \frac { \pi } { 6 } \right) ;\) tangent line to \(y = f ( x )\) at \(x = - \frac { \pi } { 6 }\)
• B)
• \(3 y + \sqrt { 3 } = 4 \left( x + \frac { \pi } { 6 } \right) ;\) secant line to \(y = f ( x )\) at \(x = - \frac { \pi } { 6 }\)
• C)
• \(3 y + \sqrt { 2 } = 4 \left( x + \frac { \pi } { 6 } \right) ;\) tangent line to \(y = f ( x )\) at \(x = - \frac { \pi } { 6 }\)
• D)
• \(3 x + \sqrt { 3 } = 4 \left( y + \frac { \pi } { 6 } \right) ;\) differential of \(y = f ( x )\) at \(x = - \frac { \pi } { 6 }\)
• E)
• \(3 y + \sqrt { 3 } = 4 \left( x + \frac { \pi } { 6 } \right) ;\) tangent line to \(y = f ( x )\) at \(x = - \frac { \pi } { 6 }\)

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