How to find the value of c?

Question

angelberina · Answer

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zepdrix · Answer

Woops, let's fix the second box first.

zepdrix · Answer

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! :)

angelberina · Answer

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

zepdrix · Answer

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

angelberina · Answer

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

zepdrix · Answer

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.