a.) find where f(x) is increasing or decreasing.

b.)find where f(x) is concave up or down.

f(x)=t-ln(t)

Question

a.) find where f(x) is increasing or decreasing.

b.)find where f(x) is concave up or down.

f(x)=t-ln(t)

anonymous · Answer

dude you are just becoming my hero

anonymous · Answer

Drawing the graph usually helps right away, but the rigorous way of solving these is like so:
take the derivative. f'(x)
Solve the equation f'(x) > 0
That tells when f(x) is increasing because it tells you when the derivative (slope) of the function is positive.

Take the second derivative. f''(x)
Solve the equation f''(x) > 0
This tell when f(x) is concave up because it tells you when the slope is increasing.

anonymous · Answer

i am going to assume this is 
$$f(t)=t-\ln(t)$$

anonymous · Answer

oh sorry i should have said this i understand how to do these but this one is tricky.
my first derivative is 1-t^2 and thats kind of where i get stuck

anonymous · Answer

yes satellite assume away

anonymous · Answer

oops not t^2 1/t

anonymous · Answer

first derivative is 
$$1-\frac{1}{t}$$

anonymous · Answer

so 1-1/t

anonymous · Answer

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