Which of the following are given by f ' ( c ) ? (a) The slope of the tangent when x = c (b) The y -coordinate of the point where x = c (c) The instantaneous rate of change of f ( x ) at x = c (d) The marginal revenue at x = c if f ( x ) is the revenue function
Which of the following are given by f ' ( c ) ? (a) The slope of the tangent when x = c (b) The y -coordinate of the point where x = c (c) The instantaneous rate of change of f ( x ) at x = c (d) The marginal revenue at x = c if f ( x ) is the revenue function
Solution Summary: The author explains that derivatives of a function have several interpretations, all of which are calculated by the same technique.
If a shark is spotted near to Brighton beach, a lifeguard will activate a siren to wai
Siren
The sound intensity, I, of the siren varies inversely with the square of the distance, d, from
the siren, where d>0.
It is known that at a distance of 1.5 metres from the siren, the sound intensity is 4 watts per
square metre (Wm).
(a)
9.
Show that / =
(b)
Sketch the curve of / on the axes below showing clearly the point (1.5,4).
20
-5-
A'(0)
A (5)
A (10)
A (15)
A (20)
-11mg/hr
-6.66mg/hr
-3.4mg/hr
-2.16mg/hr
-1.25mg/hr
4. Use a table of the values from 3. and plot the derivative y = A (t) for 0 < t< 21 hours.
%3D
Then connect your points with a smooth curve.
Examine the Function and approximate the slope of tangent through
point (1,0)
Y = - In(x)
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