# How do you sketch the graph that satisfies f'(x)>0 when x<3, f'(x)<0 when x>3#, and f(3)=5?

We know the following.

•The function is increasing in the interval

•The function is decreasing in the interval

•The function passes through the point

Considering the function is exclusively increasing in the interval

Any polynomial function of the form

The following is a graph of

Hopefully this helps!

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Here are a couple more possibilities.

HSBC244 has shown a nice graph that has derivative

Here are couple of graphs of functions that satisfy the requirements, but are not differentiable at

graph{y = -abs(x-3)+5 [-14, 22.05, -6.16, 11.85]}

graph{-(x-3)^(2/3) +5 [-5.98, 14.025, -2.15, 7.844]}

For the unconventional here is a possible graph:

(Graphed using desmos.com)

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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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