The length plus the width of a rectangle is 10. Let x represent the length. The equation for the area y of the rectangle is y = x(10 – x). The y-value of the vertex gives the (1)____________ value of the (2)__________of the rectangle.

1.
a. maximum
b. minimum

2.
a. area
b. length
c. width

Question

The length plus the width of a rectangle is 10. Let x represent the length. The equation for the area y of the rectangle is y = x(10 – x). The y-value of the vertex gives the (1)____________ value of the (2)__________of the rectangle.

1.
a. maximum
b. minimum

2.
a. area
b. length
c. width

sunnnystrong · Answer

So:
$$ y = x(10 – x)$$

Where x = the width of the rectangle & y = area of the rectangle

Solving for x--> *using calculus

$$y=-x^2+10x$$

Take the derivative -->

$$y' = -2x + 10$$

Critical points of f are when f'(x) = 0 or f'(x) is undefined so -->
x=5 is critical point where x=length of rectangle.

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