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RideAnS [48]
3 years ago
6

What is the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve y = 12 - x2? (4 points)

Mathematics
1 answer:
wolverine [178]3 years ago
7 0

Answer: 16 square units

Step-by-step explanation:

let the vertex in quadrant I be (x,y)  

then the vertex in quadratnt II is (-x,y)  

base of the rectangle = 2x  

height of the rectangle = y  

Area = xy  

= x(12 - x²)  

= -x³ + 12x  

d(area)/dx = 3x² - 12 = 0 for a maximum of area  

3x² = 12  

x² = 4  

x = ±2  

y = 12-4 = 8

So, the largest area = 2 x 8 = 16 square units

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The simplified value of the exponential expression is 2.

<h3>How to get the simplified expression?</h3>

Here we need to simplify the expression:

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First, you need to remember that:

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Then we can just write:

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If you want to learn more about exponential expressions:

brainly.com/question/11464095

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