You need to use the product rule when taking the derivative, also the chain rule.
The derivative of is .
Thus,
.
But ,
Thus,
Since divide both sides by it to get (also mutiply both sides by 8),
.
Thus,
,
Thus,
Thus,
Q.E.D.
You need to use the product rule when taking the derivative, also the chain rule.
The derivative of is .
Thus,
.
But ,
Thus,
Since divide both sides by it to get (also mutiply both sides by 8),
.
Thus,
,
Thus,
Thus,
Q.E.D.
Greetings:
Why do you believe yourself to be mistaken? Your result, i.e., a = b*sqrt(2) is correct. By the way, because your triangle is isosceles with base = (sqrt(2))(side), it is a 45-45-right triangle. This is sensible if you think of an isosceles triangle as one-half of a rhombus with side lengths, b. A bit of thought makes clear that the rhombus of greatest area is a square, half of which is an isosceles-right triangle -- and determined without the aid of Newton/Leibniz!
...for what it's worth.
Regards,
Rich B.