Question

How to find the value of c?

Answer 1

Woops, let's fix the second box first.

Answer 2

A tangent line is a straight line.

It should have the form \(\rm y=mx+b\) or \(\rm y-y_o=m(x-x_o)\) depending on whether you're used to working in slope-intercept form or point-slope form of a line.

Anyway, our tangent line shouldn't have this weird exponential in it! :)

Answer 3

So would the slope be y=(ln(2))x+1?

Answer 4

the `slope` is ln2
but the `equation` of the tangent line is y=(ln2)x+1, yes :)

Answer 5

In order to find c, would you just have to set the equation of the slop of the line to 0? I got -1/ln2

Answer 6

c is the x-intercept.
See how it intercepts the x-axis?

A line crosses the x-axis when it's y-value is zero.\[\large\rm y=(\ln2)x+1\]\[\large\rm 0=(\ln2)x+1\]Solve for x to find your c.

Yes, good.