# How do you find the local extremas for #g(x) = - |x+6|#?

Differentiability is a stronger condition than continuity

You cannot use calculus as although the function is continuous everywhere, it is not differentiable everywhere, and specifically it is not differentiable at the extrema that we seek (which happens to be a maximum)

graph{-|x+6| [-10, 10, -5, 5]}

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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.

- What are the critical values, if any, of # f(x)=x^3 + 6x^2 − 15x#?
- Does the function #f(x)=x^2 + 2x +15# have a maximum or minimum?
- What are the global and local extrema of #f(x) = e^x(x^2+2x+1) # ?
- Is #f(x)=(x^2-2)/(x-1)# increasing or decreasing at #x=2#?
- How do you find the absolute maximal and minimal values of #f(x)=x^3−6x^2+9x+4# on the interval #[−1, 5]#?

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