Tangent Lines and Normal Lines Worksheet with Answer Key

What's on the worksheet

1. Find the tangent line to each curve at the given input.
   y = x^4 - 3x, \; x = -1y = \dfrac{8}{\sqrt{x}}, \; x = 4y = x\sqrt{x}, \; x = 4
2. Let $f
3. Find every point of y = 4x where the tangent line is parallel to the secant line through (1, 4) and (4, 1), and write each of those tangent lines.
4. Find every value of the constant c for which the x-axis is tangent to the graph of y = 3x^4 - 4x³ - 12x² + c, and give the point of tangency for each.
5. Find every line through the point (−9, 0) that is tangent to y = √(x).
6. Find every normal line to y = x² that passes through the point (0, 92).
7. Let $f