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Algebra
Question

For \( f ( x ) = x ^ { 4 } - 4 x ^ { 3 } + 6 \) fi...

For \( f ( x ) = x ^ { 4 } - 4 x ^ { 3 } + 6 \) find the following. (A) \( f ^ { \prime } ( x ) \) 

(B) The slope of the graph of \( f \) at \( x = 1 \) (C) The equation of the tangent line at \( x = 1 \) (D) The value(s) of \( x \) where the tangent line is horizontal (A) \( f ^ { \prime } ( x ) = 4 x ^ { 3 } - 12 x ^ { 2 } \) 

(B) At \( x = 1 \) , the slope of the graph of \( f \) is \( - 8 . \) (C) At \( x = 1 \) , the equation of the tangent line is \( y = - 8 x + 11 \) . (D) The tangent line is horizontal at \( x = \square \) 

(Use a comma to separate answers as needed.) 

Answer

(a) 4x\(^{3}\) - 12x\(^{2}\)

(b) -8

(c) y = -8x +11

(d) x = 2

Solution
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