Question

y = 2x³ - 15x² + 36x + 1 , Find maxima or minima ?
Pls provide full steps !!

Answer 1

Answer:

dy / dx = 0

d / dx ( 2x³ - 15x² + 36x + 1 ) = 0

《 6x² - 30 x + 36 = 0 》

x² - 5x + 6 = 0

x² - 3x - 2x + 6 = 0

x(x - 3) - 2(x - 3) = 0

(x - 2) (x - 3) = 0

x = 2 , 3 .

NOW,

d²y / dx² = d / dx ( 6x² - 30 x + 36 )

d²y / dx² = 12 x - 30 .

putting the values of x :-

AT X = 2 ,

d²y / dx² = ( 12 × 2 ) - 30 = -6 < 0 .

at x = 2 , y is maximum.

AT X = 3 ,

d²y / dx² = ( 12 × 3 ) - 30 = 6 > 0 .

at x = 3 , y is minimum.

y(max) = 2(2)³ - 15(2)² + (36 × 2) + 1

= 16 - 60 + 72 + 1

y(max) = 29 .

y(min) = 2(3)³ - 15(3)² + (36 × 3) + 1

= 54 - 135 + 108 + 1

y(min) = 28 .

therefore, maxima = 29.

and minima = 28 .

Answer 2

Answer:

here Maxima 29 and minima 29