# What are the points of inflection, if any, of #f(x) = 5x^3 + 30x^2 - 432x #?

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

To find the points of inflection, we need to find the second derivative of the function and then solve for where it equals zero.

The second derivative of ( f(x) = 5x^3 + 30x^2 - 432x ) is ( f''(x) = 30x + 60 ).

Setting ( f''(x) ) equal to zero and solving for ( x ), we get ( 30x + 60 = 0 ).

Solving for ( x ), we find ( x = -2 ).

So, the point of inflection is ( (-2, f(-2)) ).

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

To find the points of inflection of the function ( f(x) = 5x^3 + 30x^2 - 432x ), we first need to find the second derivative of the function.

The first derivative of ( f(x) ) is: [ f'(x) = 15x^2 + 60x - 432 ]

The second derivative of ( f(x) ) is: [ f''(x) = 30x + 60 ]

Now, to find the points of inflection, we set the second derivative ( f''(x) ) equal to zero and solve for ( x ): [ 30x + 60 = 0 ] [ 30x = -60 ] [ x = -2 ]

So, the point of inflection is at ( x = -2 ).

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.

- Is #f(x)=-3x^3+4x^2+3x-4# concave or convex at #x=-1#?
- How do you sketch the graph #y=sqrt(1+x^2)# using the first and second derivatives?
- How do you find the inflection points of the graph of the function: # f(x)=x^(1/3)#?
- How do you find the x coordinates of all points of inflection, final all discontinuities, and find the open intervals of concavity for #y=(2x+3)^2(x+1)^2# for #[-10,0]#?
- How do you sketch the curve #y=x^2+1/x# by finding local maximum, minimum, inflection points, asymptotes, and intercepts?

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