AS level Maths Question regarding curves.?

Question

Find the values of k for which the line y=kx-4 is tangent to the curve y=x^2 + x


Thanks, I am looking for the general method for solving, not the answer,

Answer 1

You need to figure out the equation of the tangent to the curve in order to find the value of k.



The gradient dy/dx= 2x+1 ,which is equal to k.( In y=mx+c, m=gradient=k)

You need to know the co-ordinates of the point at the tangent, either the x or y value inorder to solve this.

Answer 2

The slope of lines tangent to the curve y = x^2 + x can be found by finding y'.



In this case, y' = 2x + 1. What is the slope of the line y = kx - 4?



Then you have to find the ordered pair(s) (x, y) which are common to both the curve and the line.

Answer 3

the line y = x - 3 has a gradient of a million (from y = mx + c), that's the gradient of the traditional as properly, because of the fact it particularly is parallel. as a result gradient of the traditional is -a million. The gradient of the curve = dy/dx = 6x - 2. as a result 6x - 2 = - a million Rearrange... 6x = a million ..... x = a million/6 replace into unique equation of curve... y = 3 x (a million/6)^2 - 2 x (a million/6) - a million = a million/12 - a million/3 = -0.25 -> whilst x = a million/6, y = -0.25 "y=mx+c" -> -0.25 = -a million x (a million/6) + c Rearrange -> c = - a million/12 so equation is y = - x - a million/12 or 12y + 12x + a million = 0