math help

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alexandra.vo

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a little stumped on this question. I got 1.00 as the answer. Is it right or wrong?

Suppose we want to fit a rectangle inside the triangle whose three corner points are (0, 0), (2,0) and (0,1). The edges of the rectangle are parallel to the x and y axes.
Find the maximum area of the rectangle.
 
alexandra.vo said:
a little stumped on this question. I got 1.00 as the answer. Is it right or wrong?

Suppose we want to fit a rectangle inside the triangle whose three corner points are (0, 0), (2,0) and (0,1). The edges of the rectangle are parallel to the x and y axes.
Find the maximum area of the rectangle.
Click to expand...
Please post your solution.
 
Ok, I've also got one more question if you could check for me. Is my answer correct?
 

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no... the graph doesn't even show anything special going on at x=1

try again
 
I honestly though 1 was the answer but thats wrong so I thought it was maybe -1 then? I've looked at the graph again and i'm thinking the function may be minimised now?
 
alexandra.vo said:
I honestly though 1 was the answer but thats wrong so I thought it was maybe -1 then? I've looked at the graph again and i'm thinking the function may be minimised now?
Click to expand...
I have to ask - do you know the difference between a graph of a function and a graph of the derivative of a function?
 
I am going through some maths practise before the teaching year just to try and get a head start as i'm a quite slow learner! I kind of rushed through the calculus section which is probably why I'm so confused about this question.
 
Beer soaked recall follows.
alexandra.vo said:
a little stumped on this question. I got 1.00 as the answer. Is it right or wrong?

Suppose we want to fit a rectangle inside the triangle whose three corner points are (0, 0), (2,0) and (0,1). The edges of the rectangle are parallel to the x and y axes.
Find the maximum area of the rectangle.
Click to expand...
Line from (2,0) to (0,1): y-0=(0-1)/(2-0)*(x-2)
Solve for y and substitute y into Area=x*y ....
 
alexandra.vo said:
I am going through some maths practise before the teaching year just to try and get a head start as i'm a quite slow learner! I kind of rushed through the calculus section which is probably why I'm so confused about this question.
Click to expand...
In my opinion. if there is any section in mathematics that you should NOT rush through, it is introductory Calculus. You need to understand every concept if you are to build on them and have success at a higher level. Emphasis is on understanding, not just doing or following procedures.
 
I will ask the question that lev888 asked but slightly different. Do you know the difference between a function f(x) and its derivative f'(x)?

Given a function f(x) can you explain what f'(x) is?
 
The derivative of the function is negative for x<-1. What does that tell you about the function for x< -1? The derivative of the function is positive for x> -1. What does that tell you about the function for x> -1?

In general, what does the derivative of a function tell you about the function?
 
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