Find $f ^ { ( 4 ) } ( x )$ if $f ( x ) = x ^ { 5 } - 7 x ^ { 4 } + 4 x ^ { 3 } - 6 x ^ { 2 } + 11 x - 7$ .
A) $f ^ { ( 4 ) } ( x ) = 60 x ^ { 2 } - 168 x + 24$
B) $f ^ { ( 4 ) } ( x ) = 120 x - 168$
C) $f ^ { ( 4 ) } ( x ) = x ^ { 2 } - 7 x$
D) $f ^ { ( 4 ) } ( x ) = x ^ { 2 } - 7 x + 4$

Question

Quizplus · Accepted Answer

To find the fourth derivative $f^{(4)}(x)$ of the given function $f(x) = x^5 - 7x^4 + 4x^3 - 6x^2 + 11x - 7$, we differentiate it four times. The first derivative $f'(x) = 5x^4 - 28x^3 + 12x^2 - 12x + 11$, the second derivative $f''(x) = 20x^3 - 84x^2 + 24x - 12$, the third derivative $f'''(x) = 60x^2 - 168x + 24$, and the fourth derivative $f^{(4)}(x) = 120x - 168$.

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

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