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Question 62061: I am not sure what this problem means so I don't know how to answer it, could someone help me please?
The number e is the value of x in the equation y =2^x, where the slope of the line just grazing the curve at the point (0,1) equals 1. Is this true or false?
Found 2 solutions by venugopalramana, stanbon:
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! I am not sure what this problem means so I don't know how to answer it, could someone help me please?
The number e is the value of x in the equation y =2^x, where the slope of the line just grazing the curve at the point (0,1) equals 1. Is this true or false?
y=2^x
dy/dx=(2^x)ln(2)...at x=0...the slope is 2^0*ln(2)=ln(2)
but slope is given as 1.
so it is not correct.
at x=e ,the slope is 2^e*ln(2)
but thee is a contradiction in the poblem..it say value of x=e and also says the point is (0,1)...which means x=0...both of whih are contradictory.
IF THE PROBLEM IS Y=A^X...FIND A WHERE SLOPE OF TANGENT AT (0,1) IS 1.
THEN , WE GET SLOPE = DY/DX = A^X*LN(A)....AT X =0....SLOPE = LN(A)=1
HENCE A=E..WHICH IS OK
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! The number e is the value of x in the equation y =2^x, where the slope of the line just grazing the curve at the point (0,1) equals 1. Is this true or false?
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Rewrite as
2=e^(ln2)
Rewrite the equation as
y=e^(xln2)
Take the derivative to get:
y'=2^x(ln2)
Then
y'(0)=(1)ln2=ln2
But ln2 is not 1.
So the answer is "false"
Cheers,
Stan H.
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