Differentiation Question

Question

Let f(x) = √(4x-3), Determine the equation of the tangent to f that passes through the origin (0,0)

Answer 1

Call the point of tangency [x, sqrt(4x - 3)]

The slope of the straight line from this point through the origin is sqrt(4x - 3)/x

 

f'(x) = 2/sqrt(4x - 3)

 

Therefore: sqrt(4x-3)/x = 2/sqrt(4x - 3)

4x - 3 = 2x => x = 3/2

 

The slope at x = 1/2 is (2/3)√3 and the equation of the tangent is y = (2x/3)√3.