Find the equation of the normals to the curve y=2x^2 - 7 when x=1 and x= -1. Calculate the coordinates of the point if intersection of these 2 normals.
8ve differentiated and got dy/dx= 4x
what to do after this?
do I sub x into the first equation or the gradient? How do I get the gradient after that then?
If you are given a problem like this then you are expected to know that a line perpendicular to a curve has slope equal to negative one divided by the derivative at that point. Yes, evaluate the derivative at -1 and 1, then take the negative reciprocal to find the slopes of the two lines. Can you find the equation of a line given the slope and a point on the line?
But is a normal perpendicular to the curve? i thought that was a tangent?
when x=1, y=2-7 = -5