Where do you run into your problem? Finding the tangent line? Also, there's an infinite amount of triangles that could be made. Do they specify anything else?
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