# We have #f:RR->RR,f(x)=x^2-(m-1)x+3m-4;m inRR.#Which are values of #m# for which #f(x)<0,forall x in(0,1)#?

##### 1 Answer

Dec 30, 2017

#### Explanation:

Given:

#f(x) = x^2-(m-1)x+3m-4#

Note that due to this being an upright parabola,

#f(0) <= 0" "# and#" "f(1) <= 0#

Evaluating

#3m-4 <= 0" "# and hence#m <= 4/3#

#2m-2 <= 0" "# and hence#m <= 1#

Both of these conditions hold if and only if

graph{x^2-(1-1)x+3(1)-4 [-2.427, 2.573, -1.3, 1.2]}