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.
