# How do you test #f(x)=8 x^4−9 x^3 +9# for concavity and inflection points?

To test for the concavity and inflection points you need to equate the second order derivative with zero.

Keeping in mind:

We proceed:

Now,

graph{x(16x -9) [-5, 5, -5, 5]}

Sign Chart: See image.

Now, to determine the opening of the concavity.

Negative sign indicates that the curve will open downwards. And positive sign indicates it'll open up.

And,

Hope this helps. :)

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

To test the function ( f(x) = 8x^4 - 9x^3 + 9 ) for concavity and inflection points, follow these steps:

- Find the second derivative of the function, ( f''(x) ).
- Set ( f''(x) ) equal to zero and solve for ( x ) to find potential inflection points.
- Determine the concavity of the function by analyzing the sign of ( f''(x) ) in intervals between the potential inflection points.
- Confirm the nature of the inflection points by examining the behavior of the function around these points.

If you need further clarification or assistance with any step, feel free to ask!

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

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.

- How do you find and classify all the critical points and then use the second derivative to check your results given #y=x^2+10x-11#?
- What is the second derivative of #f(x)=x/(x^2+1) #?
- For what values of x is #f(x)= 4x^3-12x^2 # concave or convex?
- How do you find the local maximum and minimum values of # f(x)=x^3 + 6x^2 + 12x -1# using both the First and Second Derivative Tests?
- If #f(x) = (5/2)x^(2/3) - x^(5/3)#, what are the points of inflection, concavity and critical points?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7