F(x)=-x^5+4x^3-x+1 # of turns # of solutions and is the right side going up or down?
1 answer:
Hello from MrBillDoesMath!
Answer:
See Discussion below.
Discussion:
From the attachment, f(x) has three real roots (and 2 complex roots).
As x increases, the polynomial approaches negative infinity and as x deceases it approaches positive infinity.
The attachment shows there are 3 "turning" or inflection points of f(x).
Thank you,
MrB
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Hi there!
There are 3 parts to this equation:
f(x)
f(x+1)
4f(x)
We must first determine these three parts separately.
<u>1) f(x)</u>
We're given that :
⇒ :
<u>2) f(x+1)</u>
Now, we must find f(x+1). To do so, add 1 to x in the original function :
⇒
<u>3) 4f(x)</u>
To find 4f(x), multiply the original function by 4:
:
<u>4) Put it all together</u>
Now, plug each of the three parts into the equation :
Factor the left side
Divide both sides by 3^x
Because this equation is true, is therefore true.
I hope this helps!