Find the area of a triangle enclosed by axes and tangent to y = 1/x
Well, let's see. If the function is , the derivative is . This tells us the gradient of the tangent line at any point x.
So the tangent line is of the form .
c is the y intercept. To find the x intercept, we'll let y = 0, and we find that
.
So the height of the triangle is c, the length is , which means the area is
So the area is
Don't think that is correct. Example consider tangent at (1,1) Gradient is -1 Equation of tangent is y=-x+2 Intercepts are both 2 Area of triangle is 2
In general consider tangent at (k,m) Gradient of tangent is -1/k^2 Get the equation of the tangent and the intercepts. Knowing also that km=1 wil get area of triangle=2