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

f '' (x) = 0
f ' (5) = 5
f (2) = −3

f '(x) =  
f (x) = 

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Expert Answer

Step 1
Given that f"(x) 0,f'(5)
5 andf(2)=-3
If f"(x) 0, then f'(x) must be a constant
So,f(x) can be written as f'(x)c
Now integrate both side as follows.
help_outline

Image Transcriptionclose

Given that f"(x) 0,f'(5) 5 andf(2)=-3 If f"(x) 0, then f'(x) must be a constant So,f(x) can be written as f'(x)c Now integrate both side as follows.

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Step 2
S(xkd=edx
f(x) GxC
Since f(5) 5 then f'(x)=
5
Again f(x)x+c, then f(x)=q+c 3
help_outline

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S(xkd=edx f(x) GxC Since f(5) 5 then f'(x)= 5 Again f(x)x+c, then f(x)=q+c 3

fullscreen
Step 3
Substitute the value of c = 5 in equation c, + c, = -3.
GC23
5c3
C28
Substitute the value of c,
5 and c, =-8 in equation f(x)= cx +c2
help_outline

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Substitute the value of c = 5 in equation c, + c, = -3. GC23 5c3 C28 Substitute the value of c, 5 and c, =-8 in equation f(x)= cx +c2

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