How do you find the value of c that satisfy the equation:

f(b)- f(a)/b-a = f'(c)

in the conclusion of the mean value theorem for the function
f(x)= 4x^2 + 4x -3 on the interval [-1,0]?

The value of c = -0.5∈ (-1,0)

Step-by-step explanation:

Step(i):-

Given function f(x) = 4x² +4x -3 on the interval [-1 ,0]

Mean Value theorem

Let 'f' be continuous on [a ,b] and differentiable on (a ,b). The there exists a Point 'c' in (a ,b) such that

Step(ii):-

Given  f(x) = 4x² +4x -3 …(i)

Differentiating equation (i) with respective to 'x'

          f¹(x) = 4(2x) +4(1) = 8x+4

Step(iii):-

By using mean value theorem

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

8c+4 = 0

8c = -4

c ∈ (-1,0)

Conclusion:-

The value of c = -0.5∈ (-1,0)

there will be 35 boys in each team. : )

b) k’(6, 4); l’(3, 3)

step-by-step explanation:

a 270° clockwise rotation maps every point (x, y) to (y, -x). (it negates the x-coordinate and then switches it and the y-coordinate.)

this means the endpoints of the side congruent to kl, k' and l', would be mapped as:

k'(-4, 6)→(6, 4)

l'(-3, 3)→(3, 3)