Question

hello, I need to solve this task
find values of a when function is Increasing from -∞ to +∞ (real numbers plurality)
function is:
y=f(x)=1/2*x^3+a*x^2+x-7
firstible i found derivative
f'(x)=3/2*x^2+2ax+1
when I showed what disertive has to be bigger than 0
3/2*x^2+2ax+1>0
how to continue or I'm doing it wrong ? please help me as soon as possible.

Answer 1

\[\frac{ 3 }{ 2 }*x ^{2}+2ax+1>0\]

Answer 2

this inequality has to be true for every single real number x

Answer 3

but only for some number a

Answer 4

so the first thing i can think of is to try some particlar value of a and see what we get

Answer 5

but how to write answer ? i need to find values and write them but I do not know how

Answer 6

dont panic,I dont either but Im trying to figure it out

Answer 7

the x^2 term is always positive or 0, so the 2ax+1 should always be positive

Answer 8

so a is greater than -1/(2x) right?

Answer 9

I think thats the answer

Answer 10

it didnt say a has to be a constant, did it? so basically does the question allow a to depend on x or not?

Answer 11

or do you just need specific examples of a rather than a general fomula

Answer 12

but a is from real numbers plurality, so if a=-100
3/2∗x2+2(-100)x+1>0

Answer 13

idk i do not understand this task i only know what disertive has to be bigger than 0
but how to write answer do no know

Answer 14

@steve816 can you continue doing and/or check my work? Im on another question

Answer 15

First of all @raimondas. it is derivative, not disertive.

Answer 16

The function will be increasing if derivative is greater than 0, so just set the derivative equal to 0 and solve the equation.

Answer 17

oh sorry im thinking about that task and do not check my english :/

Answer 18

i set derivative and equaled it to 0 already but problem is that i can't solve it

Answer 19

firstible i found derivative
f'(x)=3/2*x^2+2ax+1
when I showed what disertive has to be bigger than 0
3/2*x^2+2ax+1>0
or there are any mistakes ?

Answer 20

but I need to find values of a when function will increase but not x so there is my problem...