Use the functions f(x)=7x3−3x2−x+14 f x = 7 x 3 - 3 x 2 - x + 14 and g(x)=2x3+2x+5 g x = 2 x 3 + 2 x + 5 as examples to show that the set of polynomials is closed under subtraction.

Step-by-step explanation:

Given that the functions f ad g are defined by

and respectively.

Now subtract the given polynomials

∴

∴ are closed under subtraction,

Hence showed.

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

yes

step-by-step explanation:

yes