The table above gives values of the differentiable function f and its derivative f′ at selected values of x. Let h be the function defined by h(x)=x2ecos(3x).

Answer 1

I see that you've mentioned a table that provides values of the function \( f \) and its derivative \( f' \) at selected values of \( x \). However, I don't have access to the specific values in the table since you haven't provided them. To create a solution, I'll assume that you want to work with the function \( h(x) = x^2e\cos(3x) \), and we'll perform some calculations based on this function.

Let's proceed with the function \( h(x) \) as given:

\[ h(x) = x^2e\cos(3x) \]

We can explore a few aspects of this function:

1. **Find the Derivative \( h'(x) \):**

To find the derivative \( h'(x) \) of \( h(x) \), we'll use the product rule and the chain rule. The product rule states that if you have two functions \( u(x) \) and \( v(x) \), then the derivative of their product is given by:

\[ (u(x)v(x))' = u(x)v'(x) + u'(x)v(x) \]

In this case, \( u(x) = x^2 \) and \( v(x) = e\cos(3x) \). Let's calculate \( h'(x) \):

\( u'(x) = 2x \)

\( v'(x) = e\cos(3x)(-3\sin(3x)) = -3e\sin(3x)\cos(3x) \)

Now, apply the product rule:

\[ h'(x) = (x^2)(-3e\sin(3x)\cos(3x)) + (2x)(e\cos(3x)) \]

This is the derivative \( h'(x) \) of the function \( h(x) \).

2. **Evaluate \( h(x) \) and \( h'(x) \) at Specific Points:**

Depending on your specific problem or application, you may want to evaluate \( h(x) \) and \( h'(x) \) at certain values of \( x \). To do this, simply substitute the desired values of \( x \) into the expressions for \( h(x) \) and \( h'(x) \).

If you have specific values of \( x \) or other calculations you'd like to perform with this function, please provide more details or specific values, and I'd be happy to assist further.