You need to figure out at which x-value does the graph has a tangent line slope of -1.remember, the derivative is the slope of the tangent line. so find the derivative function and set it to equal -1 to find the x-value that will have a tangent line slope of 0.differentiate with the chain rule.
set the derivative to equal -1 and solve for x.
take log base 10 of both sides. also recall that
.
so the x-coord of the point of tangency is
.the y-coordinate of this point of tangency can be calculated using the original function:
using point-slope form, the equation of the tangent line is
the x-intercept of this tangent line is when the graph is at y=0.
this rounds off to
.choice c.