Consider the function $f(x) = 3(1 − e^x)$. Use exact values when answering the following questions:
- Find the slope of the graph of $f(x)$ at the point where it crosses the $x$-axis.
- Find the equations of the lines tangent and the perpendicular to $f(x)$ at this point.
My attempt was:
$$
0= 3(1-e^x) \\
0= 3-3e^x \\
3e^x=3 \\
e^x=1 \\
\ln(e^x)= \ln (1) \\
x=0
$$
but the answer was wrong -.-
Best Answer
It appears you have successfully found at what $x$ we have $f(x) = 0$, but the first question asks for the slope at this $x$.
Hint 1: What calculus oriented idea gives us the slope of a line at a point?
Hint 2: Now we have a point and a slope, how can we find the line given these conditions? What relation do we know about a line and the line perpendicular to it?