Homework SourseIdentify the critical numbers and find the maximum and minim
Identify the critical numbers and find the maximum and minimum value on the given interval I.f(x) = x^3 - 12x + 1; I =[-3, 5]
Solution
x3-12x+1;I=[-3,5]
to identify the critical points ,go for first derivative i.e then equate to zero,
3x2-12 =0......(2)
=>x2=4
=>x=±2
so the values we get are +2,-2
again differentiating eqn(2) we hav
6x.
go for second derivative test .....
put the values we got in 6x.
so,
putting x=+2 ,we have a positive number i.e 6,hence it is a minima.
similarly for x=-2 we have a negative number so its a maxima.
note:-hope u know that at second derivative test ,positve values result in minimas,and negative values result in maxima.
![Identify the critical numbers and find the maximum and minimum value on the given interval I.f(x) = x^3 - 12x + 1; I =[-3, 5]Solutionx3-12x+1;I=[-3,5] to identi](/WebImages/33/identify-the-critical-numbers-and-find-the-maximum-and-minim-1096331-1761578193-0.webp "Identify the critical numbers and find the maximum and minimum value on the given interval I.f(x) = x^3 - 12x + 1; I =[-3, 5]Solutionx3-12x+1;I=[-3,5] to identi")
