# How do you find values of k for which there are no critical points if #h(x)=e^(-x)+kx# where k is any constant?

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To find values of ( k ) for which there are no critical points in the function ( h(x) = e^{-x} + kx ), we first need to find the critical points of ( h(x) ) by finding its derivative and setting it equal to zero:

[ h'(x) = -e^{-x} + k ]

Setting ( h'(x) = 0 ) and solving for ( x ), we get:

[ -e^{-x} + k = 0 ]

[ e^{-x} = k ]

[ -x = \ln(k) ]

[ x = -\ln(k) ]

Now, since ( e^{-x} ) is always positive for any ( x ), ( h'(x) ) will be zero only when ( k ) is negative or zero. Therefore, for any positive value of ( k ), there will be no critical points. So, the values of ( k ) for which there are no critical points are all positive values of ( k ).

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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.

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.

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.

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