Question
Asked Oct 11, 2019
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Determine the function f satisfying the given conditions.

f ''' (x) = 12
f '' (0) = 5
f ' (0) = 2
f (0) = 3

f (x) =  x3 +  x2 +  x + 

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Expert Answer

Step 1

But given f(0)=3, so d=3 

f(x)=ax3+bx2+cx+d
f (0) d
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f(x)=ax3+bx2+cx+d f (0) d

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Step 2

Given f'(0)=2 , so c=2

f(x) ax3+bx2+cx+d
f'(x) 3ax2+2bx+c
f'(0) c
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f(x) ax3+bx2+cx+d f'(x) 3ax2+2bx+c f'(0) c

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Step 3

Given f"(0)=5

So 2b=5

O...

f (x)=ax3+bx2+cx+d
f'(x) 3ax2+2bx+c
f"(x)-6ax+2b
f"(0)-2b
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f (x)=ax3+bx2+cx+d f'(x) 3ax2+2bx+c f"(x)-6ax+2b f"(0)-2b

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