Question

Let  f(x) = 2x³ +7x² + x – 6.  Find a formula for the 4^th Taylor polynomial of f in power of (x – 2)

Answer 1

f(2)=2×2³+7×2²+2-6=16+28+2-6=40;

f'(x)=6x²+14x+1, f'(2)=24+28+1=53;

f"(x)=12x+14, f"(2)=24+14=38;

f"'(x)=12.

f(x)=40+53(x-2)+38(x-2)²/2+12(x-3)³/6=40+53(x-2)+19(x-2)²+2(x-2)³.

Taylor polynomial is f(x)=40+53(x-2)+19(x-2)²+2(x-2)³.