Find an equation of the tangent line to the graph of y = g(x) at x = 2 if g(2) = −6 and g'(2) = 5.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The slope of the line tangent to a curve g(x) at any point x is equal to g'(x).

For the function y = g(x). At the point x = 2, g'(2) = 5 and g(2) = -6

The slope of the tangent is 5 and it passes through the point (2, -6) This gives the slope of the line as (y + 6)/(x - 2) = 5

=> y + 6 = 5x - 10

=> 5x - y - 16 = 0

The required equation of the tangent is 5x - y - 16 = 0

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