Question

4. Let g be the function that satisfies g(0)=0


 and whose derivative satisfies g′(x)=2|x|.


(a) Find expressions for g(x)


and g′′(x). Ok

Answer 1

We have that for the Question "Find expressions for g(x) and g′′(x)." it can be said that expressions for g(x) and g′′(x) is

a)     $g(x) = (-x^2,x<0)\\.\ \ \ \ \ \ \ \ (x^2,x \geq0 )$

b)    $g''(x)= (-2,x<0)\\.\ \ \ \ \ \ \ \ \ \ (2,x \geq0 )$

From the question we are told

Let g be the function that satisfies g(0)=0 and whose derivative satisfies g′(x)=2|x|.

The Expressions for g(x)

Generally the equation for the g'(x)   is mathematically given as

$g'(x) = (-2x,x<0)\\.\ \ \ \ \ \ \ \ (2x,x \geq0 )$

Since

$g(x=\int{g'(x)})$

• $g(x)=g'(x) = (-x^2,x<0)\\.\ \ \ \ \ \ \ \ (x^2,x \geq0 )$

Therefore

• $g''(x)= (-2,x<0)\\.\ \ \ \ \ \ \ \ (2,x \geq0 )$

For more information on Expressions visit

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