Diagram shows the straight line touching the curve at point .
a)Find the value of
b)the coordinates of point .
You do have the straight line and the curve .
you know the straight line touches the curve at point A with the x-coordinate a
So that means at x = a (point A) the straight line has the same increase at point A as the curve.
As you know we shall solve
3 - 2a = -1
solving for a :
-2a = -1 -3
-2a = -4
a = 2
now substitute a = 2 in -a + k = 3a - a^2 (as mr fantastic was saying)
-2+k = 3*2 - 2^2
-2+k = 6-4
-2+k = 2
k = 2+2 = 4
So the straight line is y = -x+4
now substitute x = 2 and you have
y = -2+4 =2
So A = (2,2)