Given fuunction is x2+2x
Taylor Series formula is f(x) = f(a) + f'(a)(x-a) + f''(a)/2 (x-a)2 + f'''(a)/6 (x-a)3
f(3) = (3)2+2(3) = 15
f'(x) = 2x+2
f'(3) = 6+2=8
f''(x) = 2
f'''(x) = 0
Replace the obtained values in the formula
f(x) = 15+ 8(x-3) + 2(x-3)2 + 0(x-3)3
x2+2x = 15 + 8(x-3) + 2(x-3)2