# For what values of x is #f(x)=-2x^2-6x+4# concave or convex?

The function is concave everywhere.

Algebra

The graph is a parabola that opens downward. So it is concave.

Calculus

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

To determine where the function ( f(x) = -2x^2 - 6x + 4 ) is concave or convex, we need to find the second derivative of the function and then examine its sign.

First, find the first derivative of ( f(x) ): [ f'(x) = -4x - 6 ]

Now, find the second derivative of ( f(x) ): [ f''(x) = -4 ]

Since the second derivative is a constant (-4), it is negative for all real values of ( x ). This means that the function is concave down for all values of ( x ), and there are no values for which it is convex.

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 the monotonicity, extrema, concavity, and inflection points of #f(x)=lnx/sqrt(x)#?
- Find #y′′# for the curve #ln(x) + y = ln(x^2) − y^2# at #y = 0#?
- How do you find the exact relative maximum and minimum of the polynomial function of #f(x) =2x^3-3x^2-12x#?
- What are the points of inflection, if any, of #f(x) = 5x^3 + 30x^2 - 432x #?
- How do you sketch the graph #y=x^2/(1+x^2)# using the first and second derivatives?

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