Question

Please help me solve this...

please explain
OPTIONS
choose ONLY 1 answer for each blank

Blank 1: [ 1,2] , [ 4,5] , [2,3] , [3,4]
Blank 2:
remain constant and increase
Increase and increase
Remain constant and decrease
decrease and decrease
Increase and decrease
decrease and increase
Blank 3:
g(x) exceeds the value of f(x)
f(x) exceeds the value of g(x)
f(x) equals the value of g(x)
Blank 4:
never
eventually
always

Answer 1

B A B B

On Desmos, the derivative (slope) of a function can be shown by using a "prime" (apostrophe) after the function name. Here, we've drawn a dashed blue curve to show where the slope of g(x) exceeds that of f(x). g(x) has a greater slope for all values of x that are more than 4. Any interval bounded by 4 on the left end will be an interval in which the slope of g(x) exceeds the slope of f(x).

Without the graphing calculator, you can estimate that that a line parallel to f(x) will be tangent to g(x) at about x=4. Then for points to the right of that, g(x) has greater slope. Your interval [4, 5] is the only offering for Blank 1 that is appropriate.


The slope of any linear function will "remain constant", so you only need to decide if the slope of g(x) is increasing or decreasing. Your consideration of the curve already should tell you the slope will "increase" as x gets larger.


The value of f(x) is very close to the value of g(x) at x=7. They are the same when x is about x = 7.016. Up to that point, f(x) is larger. f(7) = 27; g(7) = 26.8435456. There should be no argument.


An exponential function eventually exceeds any kind of polynomial function as x gets large.