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5 cards from this section. Quick, good the night before a test.
Find the rate of change of the area of a square with respect to its side when the side is 4 cm.
Differentiate the area formula with respect to the side.
Find the rate of change of the volume of a sphere with respect to its radius when r = 3 cm.
The derivative of (4/3)πr³ is 4πr².
For a circle, A = πr². What is dA/dr when r = 5 cm?
Differentiate πr² with respect to r.
The height of a ladder's top is decreasing at 3 cm/s. What is dy/dt?
Think about the sign of the rate when something shrinks.
Water is poured at 4 cm³/s into a conical funnel held vertex down, with base radius 5 cm and height 10 cm. How fast is the water level rising when the water is 4 cm deep?
Use similar triangles to write the radius in terms of the depth before differentiating.
A man 2 m tall walks at 5 km/h directly away from a lamp post 6 m high. How fast is his shadow lengthening?
Draw the two similar triangles formed by the lamp, the man and the tip of his shadow.
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