Answer:
f(x) = x² + 2x + 1
Step-by-step explanation:
you know how to multiply 2 expressions ?
let's say in general we have
(a + b)(c + d)
you take one part of one expression and multiply it with all parts of the other expression, then you take the second part of the first expression and multiply it with all parts of the other expression, then a potential third part, then a fourth part and so on, and you add all these things together (well, depending on the actual signs, of course).
so, we get for this simple generic example
a×c + b×c + a×d + b×d
now we use that understanding for our question here.
(x+1)(x+1) = x×x + 1×x + x×1 + 1×1 = x² + x + x + 1 = x² + 2x + 1
must be continuous in order to be differentiable, so we need to have
By its definition, 
, and
so that 
.
We want the derivative to exist at 
, which requires that we pick an appropriate value for 
so that 
is also continuous. At the moment, we know
![f'(x)=\begin{cases}3x^2&\text{for }x1\end{cases}{/tex]so we need to pick [tex]f'(1)](https://tex.z-dn.net/?f=f%27%28x%29%3D%5Cbegin%7Bcases%7D3x%5E2%26%5Ctext%7Bfor%20%7Dx%3C1%5C%5Cm%26%5Ctext%7Bfor%20%7Dx%3E1%5Cend%7Bcases%7D%7B%2Ftex%5D%3C%2Fp%3E%3Cp%3Eso%20we%20need%20to%20pick%20%5Btex%5Df%27%281%29)
such that
We have
so that 
(which means we need to pick 
) and so 
90 degrees!
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Using the quadratic formula, plug a=2, b=3, and c=4 into the formula because the equation given can not be factored.
x= -3(+/-) radical (3^2-4*2*2)/2(2)
therefore, x= (-3+ radical 7 i) / 4
x= (-3- radical 7 i )/ 4.
the answer choice is 1.
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