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+10
how to continue or I'm doing it wrong ? please help me as soon as possible.

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.

raimondas. · Answer

any has ideas how to do it ? inequality should always be greater than 0 with all x values but how to find a values because i need to write them not in formula

princeharryyy · Answer

put f'(x) = 0 solve for x, check using f''(x) whether function increases r decreases at that point. if f''(x) > 0 at that point function decreases else increases.

raimondas. · Answer

but how to solve for x then in f'(x) is a, sorry for dumb questions but I'm not veri good at this.

princeharryyy · Answer

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