For f(x)=x^4-12x^3+6 find the following.A)f'(x)B)The slope of the graph of f at x=-2C)The equation of...

Aliyah Thompson

Aliyah Thompson

Answered

2022-11-23

For f(x)=x^4-12x^3+6 find the following.
A)f'(x)
B)The slope of the graph of f at x=-2
C)The equation of the tangent line at x=-2
D)The value(s) of x where the tangent line is horizontal

Answer & Explanation

Aliya Moore

Aliya Moore

Expert

2022-11-24Added 17 answers

Given f ( x ) = x 4 12 x 3 + 6
A) f ( x ) = 4 x 3 36 x 2 + 0 f ( x ) = 4 x 3 36 x 2
Answer: f ( x ) = 4 x 3 36 x 2
B)Slope of graph of f at x=-2
f ( 2 ) = 4 ( 2 ) 3 36 ( 2 ) 2 f ( 2 ) = 32 144 f ( 2 ) = 176
C) at x=-2
y = f ( 2 ) = ( 2 ) 4 12 ( 2 ) 3 + 6 y = f ( 2 ) = 16 + 96 + 6 y = 118
equation of tangent line
y y 1 = m ( x x 1 ) y 118 = 176 ( x + 2 ) y 118 = 176 x 352 y = 176 x 234
D)Since tengent line is horizontal,
Hence
f ( x ) = 0 4 x 3 36 x 2 = 0 x 3 9 x 2 = 0 x 2 ( x 9 ) = 0 x = 9  and  x 2 = 0 x = 9  and  x = 0 , 0

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