SOLUTION: Please help me solve this problem and tell me whether my answer is correct or incorrect. What is the x-intercept of the tangent to y=e^x at x=45? I got y=e^45 with the tange

Question 1015355: Please help me solve this problem and tell me whether my answer is correct or incorrect.
What is the x-intercept of the tangent to y=e^x at x=45?
I got y=e^45 with the tangent point being (45, e^45). Is this wrong?
Thanks, your help is always appreciated!
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
What is the x-intercept of the tangent to y=e^x at x=45?
I got y=e^45 with the tangent point being (45, e^45). Is this wrong?
-------------
y' = e^x
@ x = 45 --> m = e^45 at the point (45,e^45)
-----
y - y1 = m*(x-x1)
y - e^45 = (e^45)*(x - 45) is the eqn of the tangent line.
At the x-int, y = 0
----
-e^45 = (e^45)x - 45*e^45
-1 = x - 45
x = 44 --> (44,0)

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