Find an equation of the tangent line to the curve at the given point y 49 7 To find the equation of a line we need the slope of the line and a point on the line Since we are requested to find the equation of the tangent line at the point 49 7 we know that 49 7 is a point on the line So we just need to find its slope The slope of a tangent line to f x at x a can be found using the formula f x f a Ha mtan lim G In this situation the function is f x Therefore we have y mtan lim x 7 lim 249 249 Using the factorization 49 7 x 7 we have x 7 2 49 7 x 7 So we found the slope and we know that 49 7 is a point on the line Substituting these values into the point slope formula y yo m o and solving for y we can conclude that the equation of the tangent line to f x at x 49 is zia f x f a HIP man lim and a