Equation of AB ( intercept form)
ax+by=1 A line passes through the point (1,2)
a1+b2=1
a1=1−b2
a=b−2b,a>0,b>2 The area of △AOB is
Area=2ab
Area=A(b)=2(b−2)b2 Find the first derivative with respect to b
A′(b)=(2(b−2)b2)′=2(b−2)22b(b−2)−b2=2(b−2)2b2−4b Find the critical number(s)
A′(b)=0=>2(b−2)2b2−4b=0=>b1=0,b2=4We consider b>2.
If 2<b<4, then A′(b)<0,A(b) decreases.
If b>4, then A′(b)>0,A(b) increases.
The function A(b) has a local minimum at b=4.
Since the function A(b) has the only extremum for b>2, then the function A(b) has the absolute minimum for b>2 at b=4.
a=4−24=2
Areamin=22(2)=2(square units)
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