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?  

 

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  • 1 month ago
    Favorite 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?

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    • Louis1 month agoReport

      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

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  • ted s
    Lv 7
    1 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

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