Question

find values of x,for which the function f(x)=x^3+12x^2+36x+6 is increasing

Answer 1

first find the derivative
the required values are when the derivative is greater than zero

Answer 2

3x^2+24x+36 = y1

Answer 3

@ikram002p

Answer 4

right now equate this to zero and solve for x to find the turning points on the graph
and then we can find values for x the required values of x
3(x^2 + 8x + 12) = 0

Answer 5

the function will factor

Answer 6

can you factor it?

Answer 7

i did not understand

Answer 8

@cwrw238

Answer 9

to factor it you need 2 numbers whose product is 12 and when added they give 8
if we call them a and b we then get (x + a)(x + b) = 0

Answer 10

3(x+2)(x+6)

Answer 11

right so
3(x + 2)(x + 6) = 0
so x+2 = 0 and x +6 = 0
and

x = -2 or -6

Answer 12

after that

Answer 13

these are the values of x for which the graph of the function has a turning point - now we need to find the nature of these points - maximum, minimum or point of inflection

Answer 14

to do this we can find second derivative

this is derivative of 3x^2 + 24x + 36

can you do that?

Answer 15

6x+24

Answer 16

this is y2 ,right?

Answer 17

i have to go
@rational @praxer might help

Answer 18

thank u green mam @ikram002p

Answer 19

algorithm.
1. Differentiate the function.
2. equate it to zero
3. those regions where the derivative it > 0 is the region where the function is increasing.
4. You can do so, by the wavy curve method.

Answer 20

yes now the sin of this second derivative tells you if the points are maximum of minimum

x = -2: y2 = 6(-2) + 24 = 12 which id positive - so minimum
x = -6 y2 = 6(-6) + 24 = -12 - maximum

Answer 21

if it is +ve then mimimum? @cwrw238

Answer 22

so when x < -6 the function is increasing
and also its increasing when x > -2

Answer 23

yes

Answer 24

how @cwrw238

Answer 25

$$ f(x)= x^3+12x^2+36x+6$$
$$f'(x)=3x^2+24x+36$$
$$f'(x)=(x+6)(x+2)=0$$
The 2 and 6 is the points where the slope is 0 or the function is parallel to the x axis.
now
Use the wavy curve method to find the region where the function is > 0 .