Maximum Values (Leaving Cert Mathematics): Quizzes

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Maximum Values
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What is the fundamental rule for finding maximum or minimum points on a curve?

dydx=0\frac{dy}{dx} = 0

What happens to the curve at a maximum point?

Changes from increasing to decreasing

What is the first step in the method for finding maximum values?

Write down the function to maximise

For h(t)=−2t2+28th(t) = -2t^2 + 28t, how long is the rocket in flight (when does it land)?

14 seconds

For h(t)=−2t2+28th(t) = -2t^2 + 28t, what is the maximum height the rocket reaches?

98 metres

For h(t)=−2t2+28th(t) = -2t^2 + 28t, when does the rocket reach maximum height?

t=7t = 7 seconds

A farmer has 20m fencing with width xx. What is the area function?

A=20x−x2A = 20x - x^2

In the farmer problem with 20m fencing, what is the maximum area?

100 square metres

For quadratics, what does a negative coefficient of x2x^2 indicate?

Maximum (opens downward)

Which shape represents a maximum point on a curve?

∩ shape (up then down)

What is a common application of maximum value problems in business?

Maximising profit

What should you check if your answer includes negative time values?

There's likely an error

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