Question #59074

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Answer 1 · 2014-10-05T22:09:14

Let

#p(x)=ax^2+bx+c#.

By taking derivatives,

#p'(x)=2ax+b#

#p''(x)=2a#

Now, let us find #a#, #b#, and #c#.

#p''(3)=2a=6 Rightarrow a=3#

#p'(3)=2cdot3cdot(3)+b=18+b=14 Rightarrow b=-4#

#P(3)=3(3)^2-4(3)+c=15+c=16 Rightarrow c=1#

Hence,

#p(x)=3x^2-4x+1#.

I hope that this was helpful.