Questions on Summer Assignments answered...

#61. This is actually an optimization problem. Using the distance formula, write out the equation using the point given and also substitute in for y using the equation of the curve. This way you'll have an equation with only D and x. I suggest squaring both sides, because it will make taking the derivative much easier. Find find when dD/dx = 0.

#85. Use the sum and difference formulas for cosine to expand the numerator. Many of the terms will cancel out, and you can simplify nicely. You should then have something recognizable that you can evaluate the limit.

#91. This one always eludes many. Speed (a scalar) is the absolute value of velocity (a vector, meaning it has direction). So graph the absolute value of the velocity function and find the maximum.

#93. Look at the graph of the derivative and then go through the answer choices. (A) is false because the derivative is an odd function, which makes f even. (B) is also false because if f is always increasing, then that means the graph of the derivative must always be positive (above the x - axis). (C) is true because it only goes from negative to positive at the origin. (D) is false because the graph of f ' has a slope of zero (meaning f '' is zero) that means we have a POI. (E) is negative to the right of x = -(Pi), so the function is decreasing. It's not a minimum.

#94. Graph the function on the viewing window: [-4, 2] x [0, 1]. Look to see how many POIs you have.