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Average gradient: summary and exercises

  • The average gradient between two points is: y 2 - y 1 x 2 - x 1
  • The average gradient of a straight-line function is the same over any two intervals on the function
  • The average gradient of a parabolic function depends on the interval and is the gradient of a straight line that passes through the points on the interval
  • We can extend the concept of average gradient to any function

End of chapter exercises

  1. An object moves according to the function d = 2 t 2 + 1 , where d is the distance in metres and t the time in seconds. Calculate the average speed of the object between 2 and 3 seconds. The speed is the gradient of the function d
  2. Given: f ( x ) = x 3 - 6 x . Determine the average gradient between the points where x = 1 and x = 4 .
  3. Find the average gradient of each of the following functions between the points where x = 2 and x = 3
    1. f ( x ) = x 2 + 3
    2. f ( x ) = 4 x + 1
    3. f ( x ) = 2 x - 3

Questions & Answers

richa Reply
if sinx°=sin@, then @ is - ?
the value of tan15°•tan20°•tan70°•tan75° -
0.037 than find sin and tan?
Jon Reply
cos24/25 then find sin and tan
Deepak Reply
Santosh Reply
At the start of a trip, the odometer on a car read 21,395. At the end of the trip, 13.5 hours later, the odometer read 22,125. Assume the scale on the odometer is in miles. What is the average speed the car traveled during this trip?
Kimberly Reply
-3 and -2
Julberte Reply
tan(?cosA)=cot(?sinA) then prove cos(A-?/4)=1/2?2
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tan(pi.cosA)=cot(?sinA) then prove cos(A-?/4)=1/2?2
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sin x(1+tan x)+cos x(1+cot x) = sec x +cosec
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let p(x)xq
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To the nearest whole number, what was the initial population in the culture?
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The length is one inch more than the width, which is one inch more than the height. The volume is 268.125 cubic inches.
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Using Earth’s time of 1 year and mean distance of 93 million miles, find the equation relating ?T??T? and ?a.?
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Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
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what is nano technology
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preparation of nanomaterial
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Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
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Source:  OpenStax, Siyavula textbooks: grade 10 maths [caps]. OpenStax CNX. Aug 03, 2011 Download for free at http://cnx.org/content/col11306/1.4
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