Applications of Differentiation (Edexcel A-Level Mathematics): Quizzes

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Modelling with Differentiation including Optimisation
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What does the first derivative f(x)f'(x) represent?

The rate of change of the function

What does optimization involve in differentiation?

Finding max or min values of a function

How do you find critical points of a function?

Solve f(x)=0f'(x) = 0

In the second derivative test, what does f(x)>0f''(x) > 0 indicate?

Local minimum

In the second derivative test, what does f(x)<0f''(x) < 0 indicate?

Local maximum

With 100m of fencing for a rectangle, what is the maximum area?

625 square meters

In the fencing problem, what length ll maximizes the area?

25 meters

If T=7s23T = 7s^2 - 3, what is the correct differential notation?

dTds\frac{dT}{ds}

For sphere A=4πr2A = 4\pi r^2, what is dAdr\frac{dA}{dr} at r=6r = 6 cm?

48π48\pi

For sector with P=2r+200rP = 2r + \frac{200}{r}, what is the minimum perimeter?

40 cm

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