Calculate f(3), given that f(x) = x3 + f0(-1)x2 + f00(1)x + f0(-1)f(-1). Options.
A) 198 B) 197 C) 196 D) 195 E) 194
Differentiating, we compute   f0(x) = 3x2 + 2f0(-1)x + f00(1)   f00(x) = 6x + 2f0(-1):   Plugging in x = -1 into the first equation and x = 1 into the second, we obtain a system of   equations in f0(-1) and f00(1):   f0(-1) = 3 - 2f0(-1) + f00(1);   f00(1) = 6 + 2f0(-1):   Denoting f0(-1) and f00(1) by a and b respectively, we have   a = 3 - 2a + b   b = 6 + 2a:   Plugging the second equation into the first, we get   a = 3 - 2a + (6 + 2a) = 9:   Thus, b 3 - 2  + (6 + 2 )= 
<gadget id="calculator">3 - 2  + (6 + 2 )</gadget>
<output>9</output>
9:   Thus, b= 6 + 2a = 24, so   f(x) = x3 + ax2 + bx + af(-1) = x3 + 9x2 + 24x + 9f(-1):   Finally, plugging x = -􀀀1 into this equation, we get   f(-1) =-1 + 9-24 + 9f(-1)   -8f(-1) = -16   f(-1) = -2   We conclude that   f(x) = x3 + 9x2 + 24x + 18   f(3) = 33 + 9* 32 + 24 *3 + 18   = 27 + 81 + 72 + 18= 
<gadget id="calculator">27 + 81 + 72 + 18</gadget>
<output>198</output>
198   correct answer 198
<result>A</result>
Calculate f(3), given that f(x) = x3 + f0(-1)x2 + f00(1)x + f0(-1)f(-1).