Question
Find both the maximum value and the minimum value
respectively of 3a4 minus; 8a3 + 12a2 minus; 48a + 25 on the interval [0, 3].Solution
Given, f(a) = 3a4 minus; 8a3 + 12a2 minus; 48a + 25 fprime;(a) = 12a3 minus; 24a2 + 24a minus; 48 = 12(a3 minus;2a2 + 2a minus;4) = 12[a2(a minus; 2) + 2(a minus; 2)] = 12(a2 + 2)(a minus; 2) For maxima and minima, fprime;(a) = 0 =gt; 12(a2 + 2)(a minus; 2)=0 =gt; a = 2, a2 = -2 Since a2 = -2 is not possible So, a = 2 isin; [0, 3] Now we evaluate the value of f at critical point a = 2 and at the end points of the interval [0, 3] f(0) = 25 f(2) = 3 times; 24 ndash; 8 times; 23 + 12 times; 22 ndash; 48 times; 2 + 25 = 48 ndash; 64 + 48 ndash; 96 + 25 = minus;39 f(3) = 3 times; 34 ndash; 8 times; 33 + 12 times; 32 ndash; 48 times; 3 + 25 = 243 ndash; 216 + 108 minus;144 + 25 = 16 Hence, at a = 0, Maximum value = 25 At a = 2, Minimum value = -39
Section 1A (Interpretation section) was inserted to link the DSPE Act with which later statute for purposes of meanings of words and expressions?
Under Section 11(3), when parties fail to agree on an appointment procedure for a three-arbitrator tribunal, what is the default procedure?Â
Under Regulation 3(2) of the SEBI (SAST) Regulations, 2011, an acquirer who already holds 25% or more of the voting rights in a target company (but less...
Which of the following companies are required to appoint Internal Auditor to conduct internal audit of the functions and activities of the company?
A communication through WhatsApp providing record of agreement to arbitration shall:
The period of limitation for filing any suit (for which no period of limitation has been provided in Schedule of the Limitation Act) shall be:
A person who occupies the position of surety as well as agent is called as:
All of the following are sources of administrative law, EXCEPT:
A Depository Participant (DP), 'Alpha Securities,' received a written directive from the Securities and Exchange Board of India (SEBI) on February 1, 20...
Section 9(3) of the Environment (Protection) Act, 1986 allows recovery of remedial expenses together with interest at such reasonable rate as the Govern...
Relevant for Exams:
