Calculus

How to solve

The derivative f'(a) is the slope of the line that just grazes the curve at x = a. If that tangent is drawn, its slope is the answer — and for y = x² you can also compute 2a.

Steps

  1. Identify the point of tangency T and its x-coordinate a.
  2. Either read the steepness of the red tangent or compute f'(a) = 2a.

Example

Tangent to y = x² at x = 2.

  1. f'(x) = 2x.
  2. f'(2) = 4.

Answer: 4

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