Step 1 :Given the function \(y=2-6 x^{2}\), we want to find the equation of the line tangent to this function at the point \((-5,-148)\).
Step 2 :The equation of a tangent line to a function at a given point can be found using the formula \(y = mx + b\), where \(m\) is the slope of the tangent line and \(b\) is the y-intercept.
Step 3 :The slope of the tangent line is the derivative of the function evaluated at the given point. So, first we need to find the derivative of the function \(y=2-6 x^{2}\).
Step 4 :The derivative of the function \(y=2-6 x^{2}\) is \(-12x\).
Step 5 :Evaluating this derivative at \(x=-5\) gives us a slope \(m=60\).
Step 6 :We can find the y-intercept by substituting the given point into the equation of the line. This gives us the equation \(-148 = 60*(-5) + b\).
Step 7 :Solving this equation for \(b\) gives us \(b=152\).
Step 8 :Thus, the equation of the line tangent to \(y=2-6 x^{2}\) at \((-5,-148)\) is \(y=60x+152\).
Step 9 :\(\boxed{y=60x+152}\) is the final answer.