What are the end behaviors of f(x) = -2(x-17)^4? O A. Both ends go up.
O B. The left end goes down; the right end goes up.
C. The left end goes up; the right end goes down.
о
D. Both ends go down.

D. Both ends go down.

Step-by-step explanation:

f(x) = -2(x-17)^4

As x goes to -∞

f(-∞) = -2(-∞)^4 = -2 (∞) = -∞

As x goes to ∞

f(∞) = -2(∞)^4 = -2 (∞) = -∞

Both ends go to  -∞, or go down

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.