# Thread: Help with tangent exercise: If f(x)=.ax^2+bx+2 ,x<2 .gx^2+x+4 ,x>=2, then....

1. ## Help with tangent exercise: If f(x)=.ax^2+bx+2 ,x<2 .gx^2+x+4 ,x>=2, then....

If f(x)=.ax^2+bx+2 ,x<2
.gx^2+x+4 ,x>=2

find the real numbers a,b,c so that the tangent of Cf at A(2,f(2)) is vertical to the straight line m=x-3y+7 = 0

2. Originally Posted by GeorgieB
If f(x)=.ax^2+bx+2 ,x<2
.gx^2+x+4 ,x>=2
Does the above mean the following?

. . . . .$f(x)\, =\, \begin{cases}ax^2\, +\, bx\, +\, 2&\mbox{ for }\, x\, <\, 2 \\gx^2\, +\, \hphantom{b}x\, +\, 4&\mbox{ for }\, x\, \geq\, 2\end{cases}$

Is the "g" supposed to be a "c"?

Originally Posted by GeorgieB
find the real numbers a,b,c so that the tangent of Cf at A(2,f(2)) is vertical to the straight line m=x-3y+7 = 0
What is "Cf"? Does "A(2, f(2))" mean "the point A, which is located at (2, f(2))", or something else? What is the meaning of "m = x - 3y + 7 = 0"? Is this supposed to be "the line 'm', given by x - 3y + 7 = 0", or something else?

What have you tried so far? Where are you getting stuck?