Quiz Answer Key and Fun Facts
1. Let's start off with a typical basic calculus question for a warmup. What is the slope of the tangent line to the graph of y = x^3 at the point (2,8) ?
2. Consider the parabola given by the equation y = x^2 + 4x - 5. At which point on the graph of this parabola is the slope of the tangent line equal to 10?
3. The line y = 2x - 9 is tangent to the parabola y = x^2 + ax + b at the point (4,-1). What are the values of a and b?
4. Let's now consider the circle with equation x^2 + y^2 = 25. Which of the following is the equation of the tangent line to the circle at the point (3,4)?
5. Once again, consider the circle with equation x^2 + y^2 = 25. Now consider the point P with coordinates (4,7) that lies outside the circle. There are two lines that you can draw through P that are tangent to this circle. Let's call the points of tangency A and B. Which of the following is the equation of the line that passes through the points A and B?
6. At which points on the graph of the hyperbola x^2 - y^2 = 4 does the tangent line have slope equal to 5/4 ?
7. Now consider the cubic curve y = x^3 + x and the point with coordinates (-2,-10) on its graph. Suppose we draw the tangent line to the graph at this point. At what other point on the graph of y = x^3 + x does this tangent line intersect?
8. The cubic curve y = x^3 + ax^2 + bx + c passes through the point (1,3) and has tangent line y = x - 2 at the point (0,-2). What are the values of a, b, and c?
9. The cubic curve with equation y = x^3 + ax + b is tangent to the x-axis at the point (4,0). What are the values of a and b?
10. Final question: Consider the graph of the curve y = xe^(-x). At which value of x does the graph have a tangent line of minimum slope?
Source: Author rodney_indy
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