Question

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 1

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.