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Find an equation of the tangent line to the graph of 

y = g(x) at x = 5 if g(5) = −3 and g'(5) = 6

Guest Mar 26, 2017
 #1
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g'(5) = 6

This means the slope of the tangent line we're after is 6.

 

g(5) = -3

This means the tangent line passes through the point (5,-3).

 

So now all we need to do is simply find the equation for a line with a slope of 6 that passes through the point (5,-3).

 

y = mx + b

 

Plug in what we know and solve for what we don't (in this case, b).

-3 = 6(5) + b

-3 = 30 + b

-33 = b

 

Now use the slope and y intercept to make the equation.

y = 6x - 33

hectictar  Mar 26, 2017

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