# What are the points of inflection, if any, of #f(x)= 9x^3- 5 x^2-2 #?

when

When a function's second derivative changes signs, from positive to negative or vice versa, it is said to have reached a point of inflection.

At this point, the second derivative is only a potential point of inflection; make sure the second derivative truly changes sign.

Graphically, we can verify this: the concavity ought to change.

plot{(9x^3-5x^2-2) [-10, 10, -7.2, 2.8]}

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

To find the points of inflection of ( f(x) = 9x^3 - 5x^2 - 2 ), we need to find its second derivative and then solve for the values of ( x ) where the second derivative equals zero or is undefined.

( f'(x) = 27x^2 - 10x )

( f''(x) = 54x - 10 )

To find the points of inflection, set the second derivative equal to zero and solve for ( x ):

( 54x - 10 = 0 )

( x = \frac{10}{54} = \frac{5}{27} )

Therefore, the point of inflection is at ( x = \frac{5}{27} ).

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 graph of the function #y=arctan(x)#?
- Are the inflection points where f'(x) = zero or where the graph changes from concave up to concave down?
- What is the second derivative of #f(x)= 2x^3- sqrt(4-x^2)#?
- How do you find the inflection point(s) of the following equation #(1+ln(x))^3#?
- How do you find points of inflection of the function function #h(x) = −x^4 + x^2 − 1#?

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