Answer:
The value of c = -0.5∈ (-1,0)
Step-by-step explanation:
<u>Step(i)</u>:-
Given function f(x) = 4x² +4x -3 on the interval [-1 ,0]
<u> Mean Value theorem</u>
Let 'f' be continuous on [a ,b] and differentiable on (a ,b). The there exists a Point 'c' in (a ,b) such that

<u>Step(ii):</u>-
Given f(x) = 4x² +4x -3 …(i)
Differentiating equation (i) with respective to 'x'
f¹(x) = 4(2x) +4(1) = 8x+4
<u>Step(iii)</u>:-
By using mean value theorem


8c+4 = -3-(-3)
8c+4 = 0
8c = -4

c ∈ (-1,0)
<u>Conclusion</u>:-
The value of c = -0.5∈ (-1,0)
<u></u>
Ex 1:
2/5 x 4/5
Multiply both the numerators together and then multiply both the denominators together. You would multiply 2x4 which is 8 and 5x5 which is 25. Which leaves you with 8/25 and it will stay that way because you cannot simplify it further.
Ex 2:
2/5 and 5/3
Multiply across 2x5/5x3 and you end up with 10/15 which can be simplified/reduced to 2/3 because they share a common factor of 5.
Y=|x-7| because in order to go to the right you have to subtract the amount from x