Maths Question?

Question

For t:R--R,f(X)=e^x- x/e
find the coordinates of the turning point of the graph of y=f(x)


&


State the maximum domain for the function with rule f(x)=2log(e) (x-3)

(The e on the above question 2log(e) is small and below the log)

Answer 1

for the first... get the derivative...

e^x - 1/e .... and solve for the zero of this.

e^x = e^-1
then x = -1.


for the second... since the coefficient 2 also makes the argument of the ln function a square...

the maximum domain is x not equal to 3.


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Answer 2

Set y'=0:

y' = e^x - 1/e
y' = 0 -> e^x - 1/e = 0 -> e^x = e^(-1) -> x = -1

The turning point is (-1, 2/e)


Second problem:

The argument of the log must be positive, so we must have
x - 3 > 0, that is, x > 3