Question

Graph the function f(x) = -x^4 + 7x^3 - 9x^2 - 3x + 10 using graphing technology and identify for which values of x the graph is decreasing.

A. from x = -2 to x = -1
B. from x = 0 to x = 1
C. from x = 1 to x = 2
D. from x = 2 to x = 4

Answer 1

Option B

Explanation:

Plot the graph of the function
`f(x) = -x^4 + 7x^3 - 9x^2 - 3x + 10` on the coordinate plane (see attached diagram).

From the diagram, the graph of the function f(x)

• is increasing when
  `x<-0.142` and
  `1.281<x<4.111;`
• is decreaisng when
  `-0.142<x<1.281` and
  `x>4.111.`

Since
`-0.142<0<x<1<1.281,` the graph is decreasing from x = 0 to x = 1.