The intervals on which the function f(x) = ax² + bx + c (where "a" doesn't = 0) is increasing and decreasing is x>-b/2a and x<-b/2a
Given that,
We have to find the intervals on which the function f(x) = ax² + bx + c (where "a" doesn't = 0) is increasing and decreasing.
We know that,
Take the function equation,
f(x)=ax² + bx + c
The derivative of the function of x is
f'(x)=ax+b
So, f(x) is increasing when f'(x) > 0
f(x) is decreasing when f'(x) < 0
Then we can say
f'(x) > 0 , when b > 0 and a < 0
2ax + b < 0
2ax < - b
x<-b/2a
Now,
f'(x) < 0 , when b < 0 and a > 0
2ax + b > 0
2ax > - b
x>-b/2a
Therefore, the intervals on which the function f(x) = ax² + bx + c (where "a" doesn't = 0) is increasing and decreasing is x>-b/2a and x<-b/2a.
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