We are given the function <span>f(x)=sqrt of (4sinx+2) and is asked to find the first derivative of the function when x is equal to zero.

</span><span>f(x)=sqrt of (4sinx+2)

f'(x) = 0.5 </span><span>(4sinx+2) ^ -0.5 * (4cosx)

</span>f'(0) = 0.5 <span>(4sin0+2) ^ -0.5 * (4cos0)

</span>f'(0) = 0.5 <span>(0+2) ^ -0.5 * (4*1)

</span>f'(x) = 0.5 (2) ^ -0.5 * (4)

f'(x) = -.1.65

**Answer:**

C) cannot be simplified

**<u>Explanation</u>**

We want to simplify the radicals:

We can rewrite this as exponents:

Since the base are the same but are subtracting, we do not have any rule of indices for subtracting unlike indices .

Therefore the expression cannot be simplified further.

Yes we can. In Euclidean geometry, two objects are similar if they have the same shape, or one has the same shape as the mirror image of the other. More precisely, one can be obtained from the other by uniformly scaling (enlarging or reducing), possibly with additional translation, rotation and reflection. This means that either object can be rescaled, repositioned, and reflected, so as to coincide precisely with the other object. If two objects are similar, each is congruent to the result of a particular uniform scaling of the other.

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