Answer: The values for the constants are c=2, and d=-4.
explanation: We have the function f, defined as:
and
where c and d are constants.
So, if f is differentiable at x=2, then it must be continuos at x=2, therefore
Let's call this, equation 1.
On the other hand, we have that f is differentiable, therefore
and
so, we calculate
which, replacing in equation 1, gives us
Finally, the answer is that c=2, and d=-4.
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In this exercise we have to observe the axes of the graph to associate the values of X with those of Y that correspond to 0, 5, 5, -3, -5, -3, 2, 0, 0, -1, -2, 1, 1, -1, -1, -2, 2, 3, -1.
<h3>How to calculate the Cartesian plane?</h3>
Just draw two lines: one of them vertical, starting from the point until it finds the x axis; another horizontal, starting from the point until it meets the y-axis.
Then plotting the value of X on the graph we find the following for each value of X to Y:
- X= 0 ; Y= 0;
- X= 1 ; Y= 5;
- X= 2 ; Y= 5;
- X= 3 ; Y= -3;
- X= 4 ; Y= -5;
- X= 5 ; Y= -3;
- X= 6 ; Y= 2;
- X= 7 ; Y= 0;
- X= 8 ; Y= 0;
- X= 9 ; Y= -1;
- X= 10 ; Y= -2;
- X= 11 ; Y= 1;
- X= 12 ; Y= 1;
- X= 13 ; Y= -1;
- X= 14 ; Y= -1;
- X= 15 ; Y= -2;
- X= 16 ; Y= 2;
- X= 17 ; Y= 3;
- X= 18 ; Y= -1;
See more about coordinates at brainly.com/question/23450276