Question

Write down an equation of the tangent line to f(x)=(x+1)/(x-2) at a=0 (A) y=-(3)/(4)x-(1)/(2)

Answer 1

The equation of the tangent line to the given function at x = 0 is obtained by calculating its derivative, finding the slope at that point, and using the point-slope form to write the equation. The provided option (A) is incorrect as it does not follow from the steps required.

Step-by-step explanation:

The equation of the tangent line to the function f(x) = (x + 1) / (x - 2) at a = 0 can be found by first computing the derivative of f(x) to obtain the slope of the tangent line at a = 0, and then using the point-slope form of a line to write the equation. The derivative, f'(x), gives the slope of the tangent line at any point x. After finding the slope at x = a, plug this value into the point-slope equation y - y1 = m(x - x1), where (x1, y1) is the point of tangency and m is the slope of the tangent line.

Steps:

1. Calculate the derivative of f(x).
2. Find the slope at x = a by evaluating the derivative at a = 0.
3. Use the point-slope form with the slope from step 2 and the point (a, f(a)) to write the equation of the tangent line.

The correct equation of the tangent line is not given in option (A), as y = -(3/4)x - (1/2) does not result from these steps.