ble
    to use the notation $$P(x) = a_0+a_1x+a_2x^2+a_3x^3 +\cdots+a_7
    x^7.$$
  </div>

  <p>The previous two problems involved finding polynomial
  approximations to the function at $x=0$. The next problem shows
  how to move this to any other point, such as $x=1$.</p>

  <div class="problem" id="Taylor-at-1">
    Let $f(x)=e^x$.

    <ul>
      <li>Find a second degree polynomial $$T(x)=a+bx+cx^2$$ so
      that $T(1)=f(1)$, $T'(1)=f'(1)$, and $T''(1)=f''(1)$. In
      other words, give me a parabola