# Answer on Calculus Question for hsd

Question #19255

Find the second-degree Taylor polynomial for f(x)=2x2−8x+6 about x=0.

P2(x)=

P2(x)=

Expert's answer

P2(x)=f(0)+f'(0)x+f''(0)x^2/2

f(0)=6

f'(x)=4x-8, f''(x)=4

f'(0)=-8, f''(0)=4

Hence

P2(x)=6-8x+4x^2/2=2x^2-8x+6

As you can see Taylor polynomial coincides with function f(x) because function f(x) is a second degree polynomial itself

f(0)=6

f'(x)=4x-8, f''(x)=4

f'(0)=-8, f''(0)=4

Hence

P2(x)=6-8x+4x^2/2=2x^2-8x+6

As you can see Taylor polynomial coincides with function f(x) because function f(x) is a second degree polynomial itself

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