In Exercises 67–72, you will explore some functions and their inverses together with their derivatives and tangent line approximations at specified points. Perform the following steps using your CAS:


c. Find the equation for the tangent line to f at the specified point (x_0, f(x_0)).


72. y= 2-x-x³, -2 ≤ x ≤ 2, x_0 = 3/2

3. Which of the following functions grow faster than x² as x→∞? Which grow at the same rate as x²? Which grow slower?

c. √(x^4 + x^3)

132. Let f(x) = e^x / (1 + e^(2x)).

b. Find all inflection points for f.

9. True, or false? As x→∞,

c. x = O(x+5)

Use reference triangles in an appropriate quadrant to find the angles in Exercises 1–8.

5. c. arccos(√3/2)

4. Use the properties of logarithms to write the expressions in Exercises 3 and 4 as a single term.

c. 3ln ∛(t² - 1) - ln(t+1)

c. Find the slopes of the tangent lines to the graphs of h and k at (2, 2) and (−2, −2).