Find the exact value of c in the figure shown below, where the line l tangent to the graph of y = 2^x at (0, 1) intersects the x-axis.

Question

anonymous · Answer

attachment

anonymous · Answer

Differentiate to get the slope of the tangent line.

anonymous · Answer

$$
m=f'(0)
$$

anonymous · Answer

Then use the equation of a line: y=mx+c and put in the point (0,1) and the m you found than you can solve for c.

anonymous · Answer

i got $$f \prime $$$$f \prime = \ln2 * 2^x$$

anonymous · Answer

then i solved for x $$f \prime (0)=\ln2*2^0=\ln2$$

anonymous · Answer

Yeah at $x=0$

anonymous · Answer

Okay so we have points $(0,1)$ and $(c,0)$ $$
\ln 2 = \frac{1-0}{0-c}
$$

anonymous · Answer

Solve for $c$

anonymous · Answer

I got -1.442695, but when I tried to enter that it said it was wrong

anonymous · Answer

I also tried entering -1.443,0 with and without parenthesis and it was also wrong

anonymous · Answer

Perhaps you should keep the ln2 and do not write it out.

anonymous · Answer

I got it! Thank you for the help.

anonymous · Answer

:) no problemo