#6 ### Educational Text on Tangent Lines and Derivatives#### Problem 5Suppose:- \( f(-2) = 3 \), \( f'(-2) = -4 \)- \( g(-2) = 1 \), \( g'(-2) = 2 \)Let \( h(x) = f(x)g(x) \).5.1. What is the slope of the tangent line to \( y = h(x) \) at \( x = -2 \)?5.2. Find an equation for the tangent line to \( y = h(x) \) at \( x = -2 \).#### Problem 6Let \( g(x) = (x-2) e^{-x} \).6.1. Find \( g'(x) \).6.2. Determine the values of \( x \) for which the graph \( y = g(x) \) has horizontal tangents.### Explanation- **Slope of the Tangent Line**: For 5.1, use the product rule for derivatives to find the slope of the tangent line at \( x = -2 \). - **Equation of the Tangent Line**: For 5.2, utilize the point-slope form of a line using the point and slope found at \( x = -2 \).- **Derivative \( g'(x) \)**: For 6.1, apply the product rule and the chain rule to find the derivative of \( g(x) \).- **Horizontal Tangents**: For 6.2, solve for \( x \) where \( g'(x) = 0 \). Horizontal tangents occur where the derivative equals zero.

Name: #6 ### Educational Text on Tangent Lines and Derivatives#### Problem 5
Uploaded: 2024-03-05T11:52:21.000Z
Channel: Bartleby
Description: #6 ### Educational Text on Tangent Lines and Derivatives#### Problem 5Suppose:- \( f(-2) = 3 \), \( f'(-2) = -4 \)- \( g(-2) = 1 \), \( g'(-2) = 2 \)Let \( h(x) = f(x)g(x) \).5.1. What is the slope of the tangent line to \( y = h(x) \) at \( x = -2 \