Question

A.) Find the slope of the graph of f(x) = 1 - e^x at the point where it crosses the x -axis B.) Find the Equation of the tangent line to the curve at this point

Answer 1

So we need to find the x-intercepts if any
then find f'
and do f'(x-intercept)

Answer 2

i think the answer to a would be 1. Am i correct with this? I set 1 - e^x = 0 and worked from there

Answer 3

1=e^x => x=0 right?
thats the x-intercept

Answer 4

so now find f'
f'(x)=-e^x
and do f'(0)

Answer 5

so that would be -1 then

Answer 6

yep yep thats the slope :)

Answer 7

then plug in original to find the y point?

Answer 8

so y=mx+b
y=-1x+b
we know a point on the line(x=0,y=1-e^{0})=(0,0)

the y-intercept is b=0
y=-x is the tangent line