Find the equation of the tangent line to the curve at the given point. y = 5x - 2√x, (1, 3).

Solution:

Given, equation is

y= 5x - 2√x, (1, 3)

Let y = 5x - 2√x

y = 5x - 2x^1/2

dy/dx = 5 - x^-1/2

= 5 - √x/x

Let x = 1 to solve for the gradient at this point:

dy/dx = 4

Solve for the tangent equation by y - y₁ = m(x - x₁)

y - 3 = 4(x - 1)

y = 4x - 1.

Therefore, the equation is y = 4x - 1.

Find the equation of the tangent line to the curve at the given point. y = 5x - 2√x, (1, 3).

Summary:

The equation of the tangent line to the curve at the given point. y = 5x - 2√x, (1, 3) is y = 4x - 1.