# How do you find the maximum, minimum and inflection points and concavity for the function #y=1/5(x^4-4x^3)#?

Inflection point at x=0, Minima at x=3

concave up in

concave down in (0,3)

First get critical points by making

=

Now using second derivative test,

At x=0,

At x=3,

For concavity second derivative test can be used as shown below

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To find the maximum and minimum points, you first find the critical points by taking the derivative of the function and setting it equal to zero. Then, you test these critical points and the endpoints of the interval for local maximums and minimums using the first or second derivative test.

To find inflection points and concavity, you take the second derivative of the function and set it equal to zero to find points of inflection. Then, you test the intervals between these points for concavity by checking the sign of the second derivative.

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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 points of inflection, if any, of #f(x)=3x^4 − 6x^3 + 4 #?
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- How do you determine whether the function #f(x)= (x-1) / (x+52)# is concave up or concave down and its intervals?
- How do you find the inflection points of the graph of the function: #f(x) = xe^(-2x)#?
- What is the second derivative of #f(x)= 2x^3- sqrt(4x-5)#?

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