Find the slope of the tangent line to the graph of F(x)=square root (2x + 1) at (4,3 by using the limit definition.

Answer 1

Formula for the tangent line to the graph:

y-y₀=dy/dx * (x-x₀)

1. where x₀ and y₀ are coordinates of the given (4,3)

The derivate dy/dx is 1/(√(2x+1) and when putting it back in the formula for the tangent we are going to insert 4 for the x

Insert everything in the formula for the tangent and write it in the point-slope form:

y-3=(1/√(2·4+1)) · (x-4)

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y=1⁄3x + 5⁄3 is your final answer.

P.S. Let me know if you need an explanation of how to find derivative using the limit definition.