Question

$\sf\implies\: Find\: the\: points\: of\: maxima\:of\:function\:\\\\y\:=x^{3}\:-6x^{2\:}+9x\:+15\:$

Answer 1

hey mate
to get a maximum or minima of a function
differentiate it
so u will get 3x^2-12x+9=0
and find value of x by solving quadratic equation
now to find whether its maxima or minima
differentiate the equation again
#if its greater than 0 then x value is minima
#if less than 0,then x value is maxima
i hope u.understood!!

Answer 2

HELLO DEAR,



GIVEN:- y = x³ - 6x² + 9x + 15

then, dy/dx = 3x² - 12x + 9

for Maxima/minima, dy/dx = 0

so, 3x² - 12x + 9 = 0

=> x² - 4x + 3 = 0

=> x² - 3x - x + 3 = 0

=> x(x - 3) - 1(x - 3) = 0

=> (x - 1)(x - 3) = 0

=> x = 1 , x = 3

and, d²y/dx² = 6x - 12

but, [d²y/dx²]_(at x= 3) = 6(3) - 12 = 6 > 0

therefore, x = 3 is a point of minima

and [d²y/dx²]_(at x = 1) = 6(1) - 12 = -6 > 0

hence, the point of Maxima is x = 1



I HOPE IT'S HELP YOU DEAR,
THANKS