1 a) Find the slope of the graph of f(x) = 1e at the point where it crosses the x-axis.

Question

b) Find the equation of the tangent line to the curve at this point.

Answer 1

Topics:

-Geometric interpretation of derivatives

-Finding simple derivatives

-Finding tangent lines

a) When someone asks the slope of a graph at a point they really mean, "What is the slope of a line tangent to the graph at that point?" Remember the slope of the tangent line is the derivative. This derivative is the derivative of a constant.

d/dx 1 e = 0

b) To find the equation for a line you need to use two pieces of information. For a tangent line you will use the slope at the point touching the graph and the height of the graph at the point of tangency.

m = 0 (part a)

y=f(0) = e, x=0 (given)

Point Slope form if the fastest way to find the tangent line.

(y-e) = 0 ( x-0)

y = e

Yes it is the same as the function. Constant functions are the same as the functions of their their tangent lines.