Support the Monkey! Tell All your Friends and Teachers

Help / FAQ


Example 27

Find the inflection points and plot the graph of the curve y = .

Locate its x and y intercepts if they can be found and the relative maximum and minimum points.

Solution : f (x) =

\ f ' (x) = 6x2 - 24

and f "(x) = 12x

with f "(x) = 12

Since f"(x)=12(0)

                =0

and f" (0)=12 Ļ0

then (0, f (0)) i.e. (0, 5) is an

inflection point of f(x)

Put x = 0 in y =

Þ y = 5 (the y intercept)


Notice that x intercept canít be determined (why ?)

Also f ' (x) = 0 Þ x2 = 4 i.e. x = + 2

(critical points of f (x).

Now f "(-2) = 12 (-2)

= - 24 < 0

\ ' f ' has a relative maximum at x = -2

\ f (-2) = -27

\ (-2, 27) is a relative maximum point and f " (2) = 24 > 0

(2, - 27) is a relative minimum point of f (x).

[next page]

 

Index

5.1 Tangent And Normal Lines
5.2 Angle Between Two Curves
5.3 Interpretation Of The Sign Of The Derivative
5.4 Locality Increasing Or Decreasing Functions 5.5 Critical Points
5.6 Turning Points
5.7 Extreme Value Theorem
5.8 The Mean-value Theorem
5.9 First Derivative Test For Local Extrema
5.10 Second Derivative Test For Local Extrema
5.11 Stationary Points
5.12 Concavity And Points Of Inflection
5.13 Rate Measure (distance, Velocity And Acceleration)
5.14 Related Rates
5.15 Differentials : Errors And Approximation

Chapter 6





All Contents Copyright © All rights reserved.
Further Distribution Is Strictly Prohibited.

630 PinkMonkey users are on the site and studying right now.