Consider the function $f(x)=-3^x$.

1. Write the equation of the line tangent to $f(x)=-3^x$ at $x=0$.

   Hint (a):

   Evaluate $f'(0)$ to find the slope, and evaluate $f(0)$ to find the $y$-intercept. Use the point-slope formula to create the equation of the tangent line.

2. Approximate $x=0.1$ using your answer to part (a).

   Hint (b):

   Use the tangent line at $x=0$ to evaluate $x=0.1$. This will approximate $f(0.1)$. Why approximate?
   Since a tangent is a linear equation, it is easier to evaluate than $f(x)$.

3. Is your approximation an underestimate or an overestimate of the actual value? Explain.

   Hint (c):

   A concave up graph has tangent lines that are below the curve. Sketch it, you will see.
   And a concave down graph has tangent lines that are above the curve.

   Answer (c):

   Overestimate since $f^{\prime\prime}(0)=−(\ln3)^2·3^0=−(\ln3)^2<0$