# Is #f(x)=4x^5-x^4-9x^3+5x^2-7x# concave or convex at #x=-1#?

concave at x = -1

To determine if a function is concave/convex we calculate the value of f''(x) at x = a.

• If f''(a) > 0 , then f(x) is convex at x = a

• If f''(a) < 0 , then f(x) is concave at x = a

Since f''(-1) < 0 , then f(x) is concave at x = -1 graph{4x^5-x^4-9x^3+5x^2-7x [-36.52, 36.53, -18.24, 18.29]}

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

To determine the concavity of the function ( f(x) = 4x^5 - x^4 - 9x^3 + 5x^2 - 7x ) at ( x = -1 ), we need to analyze the second derivative of the function at that point.

First, find the second derivative of ( f(x) ): [ f'(x) = 20x^4 - 4x^3 - 27x^2 + 10x - 7 ] [ f''(x) = 80x^3 - 12x^2 - 54x + 10 ]

Now, evaluate ( f''(-1) ): [ f''(-1) = 80(-1)^3 - 12(-1)^2 - 54(-1) + 10 ] [ f''(-1) = -80 - 12 + 54 + 10 ] [ f''(-1) = -28 ]

Since ( f''(-1) = -28 ) is negative, the function ( f(x) ) is concave downward at ( x = -1 ).

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.

- What are the points of inflection of #f(x)=x^2-x^(1/2) #?
- What are the points of inflection of #f(x)=3ln(x^(2) +2) -2x #?
- For what values of x is #f(x)=(4x)/(x^2-1)# concave or convex?
- How do you find the inflection points of the graph of the function: #f(x)=x^4-6x^3#?
- What are the points of inflection, if any, of #f(x)=3x^5 - 5x^4 #?

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