Home > Calculus > Identifying Turning Points (Local Extrema) for a Function

What are the extrema of #f(x) = 7e^x#?

Answer 1

Charles Anctil

There are no extrema

# f(x) = 7e^x # # :. f'(x) = 7e^x #

At a max/min, # f'(x)=0 => 7e^x=0 # # :. e^x=0 #

But # e^x > 0 AA x in RR #

Hence there are no extrema!

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Luke Alvarez

The function ( f(x) = 7e^x ) has one critical point at ( x = 0 ). Since the function is continuously increasing, there are no relative extrema. However, the function has an absolute minimum at ( x = 0 ), where ( f(0) = 7 ). Therefore, ( f(x) = 7e^x ) has an absolute minimum of ( 7 ) at ( x = 0 ).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.