Applications of Differential Calculus (Grade 12 NSC Matric Mathematics): Quizzes

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Applications of Differential Calculus
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What does f′′(a)<0f''(a) < 0 indicate about the stationary point at x=ax = a?

Local maximum

Before differentiating in optimisation, the quantity must be expressed in terms of how many variables?

One variable only

What is the first step in solving optimisation problems?

Set up the problem

If s(t)s(t) represents distance, what is acceleration in terms of derivatives?

s′′(t)s''(t)

When simply mentioned, 'rate of change' typically refers to which type?

Instantaneous rate of change

What does f′′(a)>0f''(a) > 0 indicate about the stationary point at x=ax = a?

Local minimum

If s(t)s(t) represents distance at time tt, what is the velocity v(t)v(t)?

s′(t)s'(t)

To find stationary points in optimisation, what equation must be solved?

f′(x)=0f'(x) = 0

For the garden with 160m fencing and wall as one side, what is the constraint equation?

w+2l=160w + 2l = 160

What is the formula for average rate of change?

f(x+h)−f(x)h\frac{f(x+h) - f(x)}{h}

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