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Algebra
Question

For \( f ( x ) = x ^ { 4 } - 12 x ^ { 3 } + 8 \) ...

 

For \( f ( x ) = x ^ { 4 } - 12 x ^ { 3 } + 8 \) 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 

Answer

(A) \(f'(x)= 4x^3- 36x^2\)

(B) \(m= f'(- 1)= -40\)

(C) \(y= -40x- 19\)

(D) \(f'(x)= 0\Rightarrow x= 0,9\)

Solution
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