Question

Consider the function f(x)=14−eˣ Find the slope of the line tangent to the graph of 'f' at the point where the graph crosses the x-axis. The slope is:

A) -1
B) 0
C) 1
D) Cannot be determined from the information provided

Answer 1

The slope of the line tangent to the graph of f(x) = 14 - e^x at the point where the graph crosses the x-axis is -1.

Step-by-step explanation:

The slope of the line tangent to the graph of the function f(x) = 14 - e^x at the point where the graph crosses the x-axis can be found using the derivative of the function. To find the derivative, we need to apply the chain rule. The derivative of e^x is e^x and the derivative of 14 is 0, so the derivative of f(x) = 14 - e^x is -e^x. To find the slope of the tangent line, we substitute the x-coordinate of the point where the graph crosses the x-axis, which is 0, into the derivative. The slope of the tangent line is therefore -e^0 = -1.