<span>h<span>(t)</span>=<span>t<span>34</span></span>−3<span>t<span>14</span></span></span>
Note that the domain of h is <span>[0,∞]</span>.
By differentiating,
<span>h'<span>(t)</span>=<span>34</span><span>t<span>−<span>14</span></span></span>−<span>34</span><span>t<span>−<span>34</span></span></span></span>
by factoring out <span>34</span>,
<span>=<span>34</span><span>(<span>1<span>t<span>14</span></span></span>−<span>1<span>t<span>34</span></span></span>)</span></span>
by finding the common denominator,
<span>=<span>34</span><span><span><span>t<span>12</span></span>−1</span><span>t<span>34</span></span></span>=0</span>
<span>⇒<span>t<span>12</span></span>=1⇒t=1</span>
Since <span>h'<span>(0)</span></span> is undefined, <span>t=0</span> is also a critical number.
Hence, the critical numbers are <span>t=0,1</span>.
I hope that this was helpful.
12x+12 step by step below
Solve for x in 2nd equation
times -1 both sides
x-5=6y
add 5
x=6y+5
sub
5(6y+5)+4y=-26
30y+25+4y=-26
34y+25=-26
minus 25 both sides
34y=-51
divide both sides by 34
y=-3/2
sub back
x=6y+5
x=6(-3/2)+5
x=-18/2+5
x=-9+5
x=-4
(-4,-3/2) is solution
In this item, we will be able to form a system of linear equation which are shown below,
292 = 400x + y
407 = 900x + y
where x is the percent of the commission that he gets and y is the wage. The values of x and y from the equations are 0.23 and 200. This means that Justin earns a fixed wage of 200 per day and a commission which is equal to 23%.
Substituting the known values to the equation,
S = (0.23)(3200) + 200 = 936.
Therefore, Justin could have earned $936 had he sold $3,200 worth of merchandise.
