Max Min Word Problems Calculus

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Need some Math Help please….Calculus Min/Max word problems?

Find the maximum possible area of an isosceles triangle where the two equal sides are both 6 cm long.

Let the base of the triangle be 2x cm.
Then the area is y sq cm where
y = x√(36 – x²)
y’ = √(36 – x²) – x² / √(36 – x²)
.. = [36 - x² - x²] / √(36 – x²)
This has stationary values when
36 – 2x² = 0
Hence x = √18 = 3√2
When x < 3√2, y' > 0
When x > 3√2, y’ < 0
Hence x = 3√2 gives a maximum value.

Hence maximum value of y = 3√2 * √(36 - 18)
...................................... = 18

Maximum area is 18 sq cm.

Note also that the triangle with sides 6, 6, 6√2 is rightangled, and so its area is 0.5*6*6 = 18

AP Calculus Project: Application of Derivatives (Tearin’ Up My Heart)

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Category: Calculus Problems
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