Question

Using Calculus with Data in a tablePlease let me know if you have any questions regarding the material, thanks!

Answer 1

g'(0.1) = 4

Step-by-step explanation

As stated, g(x) is a composition of two functions: f(x) and 2x. To find its derivative, we have to use the chain rule,

`g^(\prime)(x)=f^(\prime)(x)\cdot(2x)^(\prime)=f^(\prime)(2x)\cdot2`

So, the derivative of g(x) = f(2x) is twice the derivative of f(x) and, therefore,

`g^(\prime)(0.1)=f^(\prime)(2\cdot0.1)\cdot2=f^(\prime)(0.2)\cdot2=2\cdot2=4`

Hence, g'(0.1) = 4.