Applications of Differentiation (HSC SSCE Mathematics Advanced): Quizzes

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Applications of Differentiation
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If a tangent has gradient mm, what is the gradient of the normal?

−1m-\frac{1}{m}

What does a negative second derivative (y′′<0y'' < 0) indicate at a stationary point?

Maximum turning point

What is dydx\frac{dy}{dx} for y=2sin⁡xy = 2\sin x?

2cos⁡x2\cos x

For y=cos⁡xy = \cos x, what is the gradient of the tangent at x=−π2x = -\frac{\pi}{2}?

11

For y=sin⁡x+cos⁡xy = \sin x + \cos x, at which xx values are stationary points on [0,2π][0, 2\pi]?

π4\frac{\pi}{4} and 5π4\frac{5\pi}{4}

What is the amplitude of y=sin⁡x+cos⁡xy = \sin x + \cos x?

2\sqrt{2}

If y′′=−2y'' = -\sqrt{2} at a stationary point, what is the nature of that point?

Maximum turning point

What is the derivative of y=tan⁡2xy = \tan 2x using the chain rule?

2sec⁡22x2\sec^2 2x

For f(x)=x−sin⁡xf(x) = x - \sin x, why is f′(x)=1−cos⁡xf'(x) = 1 - \cos x never negative?

Because cos⁡x≤1\cos x \leq 1 always

What type of symmetry does y=x−sin⁡xy = x - \sin x have?

Rotational about the origin

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Sequences and Series

Graphs and Equations

Curve-Sketching Using the Derivative

Integration

The Exponential and Logarithmic Functions

The Trigonometric Functions

Motion and Rates

Series and Finance

Displaying and Interpreting Data

Continuous Probability Distributions

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Displaying and Interpreting Data

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Sequences and Series

Graphs and Equations

Curve-Sketching Using the Derivative

Integration

The Exponential and Logarithmic Functions

The Trigonometric Functions

Motion and Rates

Series and Finance

Displaying and Interpreting Data

Continuous Probability Distributions

Show more

Displaying and Interpreting Data

Continuous Probability Distributions

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