Question

Find the point of minima if `y=x^(3)-(15)/(2)x^(2)+18x

​

Answer 1

Answer:

f(x)=2x

3

−15x

2

+36x+10→(i)

differentiatew.rtox

⇒f

′

(x)=6x

2

−30x+36

⇒f

′

(x)=0

⇒6x

2

−30x+36=0

⇒x

2

−5x+6=0

⇒x

2

−3x−2x+6=0

⇒x(x−3)−2(x−3)=0

⇒x=3,x=2

againdifferentiatew.rtox

f

′

(x)=12x−30→(ii)

Putx=2

⇒f

′

(2)=24−30=−60,x=2pointmaximum

andminimumvalueisf(2)=2×2

3

−15×2

2

+36×2+10

⇒f(2)=16−60+71+10=38

andputx=3ineq

n

(ii)

⇒f

′

(3)=36−30=6Itispointmaximum

andminimumvalueis

f(3)=2×27−15×9+36×3+10=37