Suppose f ( x ) is a function such that f (1) = 2 The domain of f is (-?,?). The
ID: 2866657 • Letter: S
Question
Suppose
f(x)
is a function such that
f(1) = 2
The domain of f is (-?,?).
The graph of f?' is
On your own graph paper make a possible sketch of the function
f(x)
.
Which of the following statements are true about the function f?
Select all that apply.
f is increasing on the interval (0,5).
The slope of f is zero at the point x = 2.5.
The slope of f is zero at the point x = 5.
f is decreasing on the interval (2.5,?).
f is increasing on the interval (??,2.5).
f is decreasing on the interval (??,0).
f passes though the point (5,0).
Suppose f(x) is a function such that f(1) = 2 The domain of f is (-?,?). The graph of f?' is On your own graph paper make a possible sketch of the function f(x) . Which of the following statements are true about the function f? Select all that apply. f is increasing on the interval (0,5). The slope of f is zero at the point x = 2.5. The slope of f is zero at the point x = 5. f is decreasing on the interval (2.5,?). f is increasing on the interval (??,2.5). f is decreasing on the interval (??,0). f passes though the point (5,0).Explanation / Answer
1) f is increasing on the interval (0,5).
Answer :
Notice the graph of the derivative given to us.
The derivative value is POSITIVE OVER 0 to 5
So, this means, the function, f INCREASES over (0 , 5)
So, TRUE
2) The slope of f is zero at the point x = 2.5.
Answer :
The derivative has a maximum value at x = 2.5
Now, the slope of f is 0 at the points where the derivative equals ZERO and this happens at x = 0 and x = 5
So, FALSE
3) The slope of f is zero at the point x = 5
Answer :
The derivative is nothing but slope of the curve at that point
Notice from the derivative graph that df/dx = 0 at x = 0 and x = 5
So, slope of f is 0 at x = 5
TRUE
4) f is decreasing on the interval (2.5,?).
Answer :
From the derivative graph, the derivative df/dx is positive over (0 , 5)
So, this means, the function has to be INCREASING over (0 , 5)
So, FALSE
5) f is increasing on the interval (??,2.5).
Answer :
I assume the "??" was actually -2
Notice the derivative is negative over (-2 , 0)
So, over this region, the function, f DECREASES
And over (0 , 5), f INCREASES
And over (5 , 6), f DECREASES again
So, FALSE
6) f is decreasing on the interval (??,0).
Answer :
I assume the "??" was actually -2
From the derivative graph, the derivative is a negative value over (-2 , 0)
So, the function, f is DECREASING over (-2 , 0)
So, TRUE
7) f passes though the point (5,0).
Answer :
The derivative passes through (5,0)
This does not mean that f must also
So, FALSE
So, the statements that are true are :
f is increasing on the interval (0,5). --> ANSWER
The slope of f is zero at the point x = 5 --> ANSWER
f is decreasing on the interval (-2,0). --> ANSWER