Answer:
f is increasing on interval (-infty, 13/4)
Inequality notation: x<13/4
In words: f is increasing on the interval of x that is less than 13/4.
Step-by-step explanation:
f is increasing on interval of x if f' of such interval is positive.
f=-2x^2+13x-8
Differentiate both sides
(f)'=(-2x^2+13x-8)'
Sum and difference rule:
f'=(-2x^2)'+(13x)'-(8)'
Constant multiple rule:
f'=-2(x^2)'+13(x)'-(8)'
Power rule (recall x=x^1):
f'=-2(2x^1)+13(1x^0)-(8)'
Constant rule:
f'=-2(2x^1)+13(1x^0)-(0)
Recall again x^1=x:
f'=-2(2x)+13(1x^0)-(0)
Recall x^0=1:
f'=-2(2x)+13(1×1)-(0)
Associative property of multiplication:
f'=-(2×2)x+13(1×1)-(0)
Performed grouped multiplication:
f'=-(4)x+13(1)-(0)
f'=-4x+13-(0)
Additive identity:
f'=-4x+13
f' is positive when -4x+13>0.
Subtract 13 on both sides:
-4x>-13
Divide both sides by -4:
x<-13/-4
x<13/4
f is increasing on interval (-infty, 13/4)
