Question

Find an equation of the tangent line to the curve at the given point using a calculator: a) y = mx + c b) y - y₁ = m(x - x₁) c) y = f' (x₁) (x - x₁) + f (x₁) d) y = f (x₁ + h) - f (x₁) / h (x - x₁) + f (x₁)

Answer 1

The equation of the tangent line to a curve at a given point can be found using the point-slope form equation.

Step-by-step explanation:

The equation of the tangent line to a curve at a given point can be found using the point-slope form equation:

y - y₁ = m(x - x₁)

where (x₁, y₁) is the given point on the curve and m is the slope of the tangent line. To find m, you can use the derivative of the curve. The derivative at the given point will give you the slope of the tangent line.

So, the correct equation in this case would be
y - y₁ = f'(x₁)(x - x₁) + f(x₁).