For a function g, we are given that g(-6) = -8 and g'(-6) = 3. What's the equation of the tangent line to...

Question

For a function g, we are given that g(-6) = -8 and g'(-6) = 3.
What's the equation of the tangent line to the graph of g at x = -6?
Choose 1 answer:
A) y + 8 = 3(x + 6)
B) y + 6 = 3(x + 8)
C) y - 3 = -8(x + 6)
D) y + 6 = -8(x - 3)

SnapAndSolve AI · Accepted Answer

The equation of the tangent line to a function at a given point is given by the point-slope form: y - y₁ = m(x - x₁), where m is the slope of the tangent line and (x₁, y₁) is the point of tangency. Here, m = g'(-6) = 3 and the point is (-6, -8). Substituting these values into the point-slope form gives: y - (-8) = 3(x - (-6)), which simplifies to y + 8 = 3(x + 6). Therefore, the correct answer is A) y + 8 = 3(x + 6).

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For a function g, we are given that g(-6) = -8 and g'(-6) = 3. What's the equation of the tangent line to...

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