...value of the tangent of the angle made by the intersection with the axis of x of the line that is drawn tangent to the curve at the point whose coordinates are x and y. Putting, therefore, inc x = 0, we obtain, 5— or, replacing b by its value a — 1 , Moreover, since...

...-~ — 3 + 3Qx — 6^, and proceed in the same wav as before, we shall get -f- = 51, and thence ux the equation of the tangent to the curve at the point whose abscissa is 4, is Y — 172 = 51 (X — 4). Putting x and y for X and Y in this, we readily get a,*—...

...derivatiTe of the ordinate of the point of tangency, with respect to x, or a = -j—,M Fig. 16. (2) is the equation of the tangent to the curve at the point (x', y'), x and y being the current co-ordinates of the tangent. Since the normal is perpendicular...

...and Q (Fig. 9), then y" — y' = dy', and x" — x' = dx'; and the equation becomes dx' v" ' 'This is the equation of the tangent to the curve at the point P, whose co-ordinates are denoted by Making y = 0, we find for the point T, where the tangent meets...

...geometrical meaning of the differential coefficient of y with respect to x, when x=4. Hence write down the- equation of the tangent to the curve at the point whose abscissa is 4. 2. Find the radius of the base of the cylinder of maximum volume, which can be cut out...

...derivative exists and is continuous. If x = a, y = b is a point on this curve, then yb = Df(a)(xa) (10.1) is the equation of the tangent to the curve at the point (a,b), where Df(a) = (d//dx)x=a. In fact, the derivative D/(a) can be defined as the unique number...

...given gradient. (a) y = x3 ; 48 (b) (с) 6 . A curve has equation y = ax2 + bx , and Зх + у + 11 = 0 is the equation of the tangent to the curve at the point ( -2, 5 ). Find the value of a and b . 1 . g(x) = mx + c is the equation of the tangent to the curve...