# how to find limit of a genertic point?

The path of a robot along a track is modeled by the curve y=2𝑥^2+1. As the robot moves, it passes through the point P (−1,3). At this point, it attempts to shoot a ball at a target located at the point (1,-5). If the ball travels along the tangent line to the curve at point P, will the ball hit the target?

i know that the ball will hit the point as the slope of the tangent is -4x

however, using the formula ( f(x+h) - f(x) ) / h and subsituting will get me 4x and not -4x.

should i use f(x-h) instead of f(x+h) if so, why?

### 2 Answers

- 1 month agoFavorite Answer
slope is 4x so what is the slope when x=-1?

So the reasont he slope of the tangent line at that point is -4 is because x is -1, if you were looking at (1,3) the slope of the tangent line would be 4

Does that help?

- ted sLv 71 month ago
y ' ( -1) = 4 ( - 1 ) = - 4....and true [ f(- 1 + h ) - f ( -1) ] / h ----> - 4....[f(x+h) - f(x) ] / h ---> 4x , and x = - 1 ====> f'(-1) = - 4

- Login to reply the answers

Sorry for the late response. To get the equation you need to use the point slope form

y - y1 = m(x - x1) where (x1, y1) is a point on the line (so (-1, 3) ) and m is the slope 4x1 where x1 is the x value of that point (so 4*-1 = -4) So working everything out gets you

y = (4*-1)x - (-4*-1)*-1 + 3