To find the equation of the tangent line to the curve y = ext{sin}(x) imes p imes 0 at a specific point, we first need to identify the point on the curve where we want to find the tangent line.
However, the given equation seems to contain a constant (p) multiplied by 0, which implies that y would always equal 0, regardless of x. If we are looking for the tangent line at a certain x-value where y is still 0, the procedure is as follows:
- Determine the point of tangency. Let’s assume we’re at point (x₀, 0).
- Next, we find the derivative of y with respect to x to obtain the slope of the tangent line. Since y = 0, the derivative is also 0, indicating that the slope of the tangent line is horizontal.
- The equation of a line in point-slope form is given by y – y₀ = m(x – x₀), where m is the slope and (x₀, y₀) is the point of tangency.
- Substituting our known values, we have:
- This simplifies to:
y - 0 = 0(x - x₀)
y = 0
Therefore, the equation of the tangent line at any point on the curve y = 0 is simply the line itself, which is y = 0. This means that for the given scenario, regardless of the actual value of x, the tangent line remains constant and horizontal along the x-axis.