Find g prime left parenthesis x right parenthesis for the given function. Then find g prime left parenthesis negative 3 right parenthesis , g prime left parenthesis 0 right parenthesis , and g prime left parenthesis 2 right parenthesis. g left parenthesis x right parenthesis equals StartRoot 4 x EndRoot

Answer: For x = 0, - 3, our expression is undefined and for x = 2, we have 0.707.

Step-by-step explanation: From the question, we have

g (x) = / sqrt{4x}

Simplifying the right-hand side, we have:

g (x) = 2x^{1/2}

Differentiating with respect to $x$ using the second principle, we have,

g' (x) = 2 * / frac{1}{2} * x^{/frac{1}{2} - 1}

= x^{-1/2}

So from the indical laws, g' (x) = x^/frac{-1}{2} = 1//sqrt{x}

For values of g' (x) when x = - 3, we have

g (x) = 1//sqrt{-3}

g (x) is undefined for values of x when x is - 3 since the square root of a negative number is not defined. However, using complex solution we have

g (x) = 1//sqrt{-3}

But / sqrt{-1} = i; then / sqrt{-3} = / sqrt (-1 * 3)

This is same as / sqrt (-1) * / sqrt (3)

And then we have 1.732i

For x = 2, we have

g' (2) = 1//sqrt (x)

= 1//sqrt (2) = 0.707

For x = 0, we have

g' (0) = 1//sqrt (0)

= 1/0

Here again for x = 0, our expression is undefined.