enjoy:
consider the function y = 1/x
let A be a point on the function
the tangent through A intersects the coordinate axes at C(c,0) and D(0,d)
prove that the area of this triangle is the same no matter where A is located and find that area
enjoy:
consider the function y = 1/x
let A be a point on the function
the tangent through A intersects the coordinate axes at C(c,0) and D(0,d)
prove that the area of this triangle is the same no matter where A is located and find that area
Hello,
Did you draw a sketch ?
The area of the triangle OCD is defined by . Do you agree ?
Distance OD is d and distance OC is c, so
Now, you may know the equation of the tangent to a function. Let m be the absciss of A.
The equation will be :
Knowing that , determine the equation.
You know that C and D are on this tangent. Hence, replace their coordinates in it and isolate c and d.
So you will have and with respect to m.
Substitute in the expression of and conclude
It's long because I've given all the elements, so try to do and when you can't move on, post