# What are the points of inflection of #f(x)=(3x^2 + 8x + 5)/(4-x) #?

Even though there are no inflexion points, there still are minimum

Let's get started,

Check: graph{(3x^2 + 8x + 5)/(4-x) [-320, 320, -160, 160]}

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

To find the points of inflection of ( f(x) = \frac{3x^2 + 8x + 5}{4-x} ), first, determine the second derivative, then find where it equals zero, and finally check the concavity to identify the points of inflection.

First derivative: ( f'(x) = \frac{d}{dx} \left( \frac{3x^2 + 8x + 5}{4-x} \right) )

Second derivative: ( f''(x) = \frac{d^2}{dx^2} \left( \frac{3x^2 + 8x + 5}{4-x} \right) )

After finding the second derivative, solve for ( x ) when ( f''(x) = 0 ). These values represent possible points of inflection.

Then, determine the concavity of ( f(x) ) around these points to confirm if they are indeed points of inflection. This can be done by evaluating the second derivative's sign around each candidate point.

Once the points of inflection are identified, their corresponding ( y )-coordinates can be found by substituting the ( x )-values into the original function ( f(x) ).

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

- For what values of x is #f(x)=(x-3)(x-1)(x-2)# concave or convex?
- For what values of x is #f(x)=(-2x)/(x-1)# concave or convex?
- How do you sketch the graph that satisfies f'(x)>0 when x does not equal 2, f(2)=1?
- What is the second derivative for #y(x)=5e^(pi x)+cos (y(x))# ?
- How do you find points of inflection and determine the intervals of concavity given #y=tan^-1x#?

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