Grade 12 · Math
Use a derivative to find a tangent line
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For f(x) = x2 + 4, the tangent line at x = -2 is y = -4x + b. What is b?
- -1
- 0
- 2
- 1
See the answer & why
0
The derivative gives slope 2x, or -4 at x = -2. The tangent passes through (-2, 8); b = 8 − (-4)(-2) = 0.
A little hint: A tangent line uses the derivative for slope and passes through the point on the original curve.
Evaluate the original function at the chosen x-coordinate to obtain a point on the curve.
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