Answer:
53.13
Step-by-step explanation:
Answer:
Multiply each le and divde from the one on the left
Step-by-step explanation:
<span>4 ⋅ 6 + 5 ⋅ 7 + 6 ⋅ 8 + ... + 4n( 4n + 2) = 4(4n+1)(8n+7)/6
is false because it isn't even true when n=1.
4 ⋅ 6 = 4(4*1+1)(8*1+7)/6
24 = 4(5)(15)/6
24 = 50
Also 4n(4n+2) is not even the correct formula
for the nth term. The correct nth term formula
of 4 ⋅ 6 + 5 ⋅ 7 + 6 ⋅ 8 + ...
is (n+3)(n+5). So it's wrong all the way around.</span>
Use both!
You want to minimize <em>P</em>, so differentiate <em>P</em> with respect to <em>x</em> and set the derivative equal to 0 and solve for any critical points.
<em>P</em> = 8/<em>x</em> + 2<em>x</em>
d<em>P</em>/d<em>x</em> = -8/<em>x</em>² + 2 = 0
8/<em>x</em>² = 2
<em>x</em>² = 8/2 = 4
<em>x</em> = ± √4 = ± 2
You can then use the second derivative to determine the concavity of <em>P</em>, and its sign at a given critical point decides whether it is a minimum or a maximum.
We have
d²<em>P</em>/d<em>x</em>² = 16/<em>x</em>³
When <em>x</em> = -2, the second derivative is negative, which means there's a relative maximum here.
When <em>x</em> = 2, the second derivative is positive, which means there's a relative minimum here.
So, <em>P</em> has a relative maximum value of 8/(-2) + 2(-2) = -8 when <em>x</em> = -2.
I’m pretty sure the answer is no
