Find $f ^ { ( 4 ) } ( x )$ if $f ( x ) = x ^ { 5 } - 8 x ^ { 4 } + 7 x ^ { 3 } - 7 x ^ { 2 } + 7 x - 4$
A) $f ^ { ( 4 ) } ( x ) = 120 x - 192$
B) $f ^ { ( 4 ) } ( x ) = x ^ { 2 } - 8 x$
C) $f ^ { ( 4 ) } ( x ) = x ^ { 2 } - 8 x + 7$
D) $f ^ { ( 4 ) } ( x ) = 60 x ^ { 2 } - 192 x + 42$

Question

Quizplus · Accepted Answer

To find the fourth derivative $f^{(4)}(x)$ of the given function $f(x) = x^5 - 8x^4 + 7x^3 - 7x^2 + 7x - 4$, we differentiate it four times. The derivatives are as follows: $f'(x) = 5x^4 - 32x^3 + 21x^2 - 14x + 7$, $f''(x) = 20x^3 - 96x^2 + 42x - 14$, $f'''(x) = 60x^2 - 192x + 42$, and $f^{(4)}(x) = 120x - 192$.

Find f(4)(x)f ^ { ( 4 ) } ( x )f(4)(x)

Find $f ^ { ( 4 ) } ( x )$