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>
Answer:
Y1 intercept = 2
(0,2) (3,-7)
m= (-7 - 2) / (3-0) =-9/3 = - 3
Then y = - 3x + 2
Y2 intercept = - 8
(0,-8) (3,-7)
m = (-7 - - 8) / (3-0) = 1/3
Then y= (1/3)x-8
Answer:
1/3
Step-by-step explanation:
(2/3)x^2 -6x + 15 = 0
Using the quadratic formula:
x = [-b +-sq root(b^2 - 4 *a*c)] / 2a
x= [--6 +-sq root(36 -4*(2/3)*15] / 2*(2/3)
x= [6 +-sq root 36 -40] / (4/3)
x1 = 4.5 + (2i / (4/3))
x1 = 4.5 + 1.5i
x2 = 4.5 - (2i / (4/3))
x2 = 4.5 - 1.5i