Question

Given: x^4-7x^3+6x^2+8x+9
a) Determine the x- and y-coordinates of the lowest point on the graph.
b) Find the Highest and lowest values of f(x) over the interval -10<=x<=10

Answer 1

The only way I know how to figure this out is by graphing

Answer 2

The only way I can think of getting b) is by calculus but I dont think this is a calculus problem

Answer 3

a) ( 4.48088, -61.3244 ) is the lowest point on the plot and lies between, x=-10 and x=10 in the fourth quadrant.

The highest values at x=-10 and x=10 are the y coordinates in the points shown below respectively:
b) ( -10, 17529 ), ( 10, 3689 )

The attached plots show the curve between x=-1.5 and x=6, and x=-8 and x=10 respectively.

Answer 4

Mathematica 8 was used to effect a numeric solution of the first derivative, of the problem equation, set to zero for the roots.
\[\text{NSolve}\left[4 x^3-21 x^2+12 x+8=0,x\right] \]\[\{x\to -0.386301,x\to 1.15542,x\to 4.48088\} \]