# A rectangle has dimensions 0.7x and 5 - 3x. What value of x gives the maximum area and what is the maximum area?

##### 2 Answers

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#### Explanation:

Given dimensions of the rectangle are:

Area of the rectangle

Area of the rectangle

To maximize the area the first derivative is to be set equal to

or

or

To confirm that it is a maximum we need to evaluate second derivative at the obtained value of

Second derivative

Maximum Area

Maximum area =

(

#### Explanation:

Let the area be

From the question the area is:

Rate of change in

Using calculus: shortcut method

Rate of change is zero at maximum area

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~

to find the fractional solution:

so

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Thus the exact area is

The approximate area is