The 3rd–degree Maclaurin polynomial for f(x)=e2x is P3(x)=1+2x+2x2+34x3. Determine the largest symmetric interval centered at 0 on which P3(x) approximates f(x) with an error not exceeding 0.001.
a) [−0.20,0.20]
b) [−0.16,0.16]
c) [−0.18,0.18]
d) [−0.12,0.12]