Polynomial Curve Sketching

For a function g(x), g''(3)=-8 indicates that g(x) is ____________ at x=3.

• increasing

• decreasing

• concave up

• concave down

What are the intervals of the graph increasing for f(x) = 2x⁴- 4x² + 1

• (-1,0)

• (0,1)

• (-∞,-1) and (0,1)

• (1,∞) and (-1,0)

What is the maximum value of f(x) = x³ - 3x² - 1 on the interval [-3, 2]?

• 0

• -1

• 2

• 5

Which graph is the derivative of the top graph?

• A

• B

• C

• D

Given the polynomials: c(x)=x^3-15x^2+72x-112 a(x)=x^2+5 k(x)=x^3+21x^2+144x+324 e(x)=2x^2+28x+96 match each polynomial function to its graph.

• 
• 
• 
• 

Which point does not represent a zero of a polynomial?

• (-2, 0)

• (-1, 0)

• (0, 4)

• (2, 0)

f' is given, which could be f?

• A

• B

• C

If f '(3) = 0 and f"(3) < 0, then which of the following must be true?

• There is a local max at x=3

• There is a local min at x = 3

• There is an inflection point at x = 3

• There is an x-intercept at x = 3

The graph shown is the DERIVATIVE of f. From the derivative's graph, identify the interval graph where f (the original function) is concave up.

• (-1,1) & (3,4)

• (-3,-2)

• (-2,-1)

• (-3,-1) & (1,3)

Which function is graphed?

• (x - 4)(x + 2)(x - 8)=y

• (x - 4)(x - 2)(x + 8)=y

• (x - 4)(x + 2)(x + 8)=y

• (x + 4)(x + 2)(x + 8)=y