Optimization & Modelling

[Swarnila]

I am confused about the explanation. Why draw a line from (0,0) for g(v) and not elsewhere, for instance (0,1)? And how did the person conclude that the line with the smallest slope is tangent to f(v)? Any help will be appreciated.

 

[Harry_the_cat]

View attachment 22432I am confused about the explanation. Why draw a line from (0,0) for g(v) and not elsewhere, for instance (0,1)? And how did the person conclude that the line with the smallest slope is tangent to f(v)? Any help will be appreciated.

See how they have conveniently put the 0s on the numerator and denominator (The expressions would not be equal if these weren't 0s.) This now looks like (diff in ys)/(diff in xs) which is the gradient formula from (0, 0) to the curve.
For your second question, try drawing another line from (0,0) to the curve with a smaller slope than the slope of the tangent.

 

[Swarnila]

See how they have conveniently put the 0s on the numerator and denominator (The expressions would not be equal if these weren't 0s.) This now looks like (diff in ys)/(diff in xs) which is the gradient formula from (0, 0) to the curve.
For your second question, try drawing another line from (0,0) to the curve with a smaller slope than the slope of the tangent.

Thanks a lot for your explanation! I understand it now.