Consider the function f(x) = 3(1 − e^x)

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

(b) Find the equation of the tangent line to the graph of f(x) at the point in part (a). Use y as the dependent variable.

(c) Find the equation of the line which is perpendicular to the tangent line in part (b) and passing through the point in part (a). This line is called a normal line. Use y as the dependent variable.

Question

Consider the function f(x) = 3(1 − e^x)

(a) Find the slope of the graph of f(x) at the point where it crosses the x-axis.

(b) Find the equation of the tangent line to the graph of f(x) at the point in part (a). Use y as the dependent variable.

(c) Find the equation of the line which is perpendicular to the tangent line in part (b) and passing through the point in part (a). This line is called a normal line. Use y as the dependent variable.

loser66 · Answer

Any idea?

tkhunny · Answer

Have you considered the first derivative?

mathmale · Answer

Determine the x-coordinate of the point at which the graph crosses the x-axis.
Find the first derivative of the given function, and then substitute the x-value you've just found.  Your result will represent the slope of the graph of the original function.