1/√3

-1/√3

±1/√3

The MVT doesn't apply

All 3 statements are true

Only 2 and 3 are true

Only 1 is true

None of the statements are true

y= tan(x) [-π/3, π/3]

y = sin(x) [-π,2π]

y= log(x) [-1,1]

y = 1/x [4,7]

y = cot(x) [-π,2π]

y = $\frac{x^2+5x+3}{x-1}\ \ \ \ \ \ \left[0,3\right]$

y = $\left(7x^2+6x-3\right)\left(x^6-3x+7\right)\ \ \ \ \ \ \ \ \left[2,9\right]$

y = $\frac{\sin\left(x\right)}{x-1}\ \ \ \ \ \ \ \ \ \left[0,4\right]$

a point c ∈ (a,b) where tangent when drawn is parallel to X-axis.

a point c ∈ [a,b] where tangent when drawn is parallel to X-axis

a point c ∈ (a,b) where tangent when drawn is parallel to the chord joining end points of the curve y = f(x).

a point c ∈ [a,b] where tangent when drawn is parallel to the chord joining end points of the curve y = f(x).

a point c ∈ [a,b] where tangent when drawn is parallel to the chord joining end points of the curve y = f(x).

a point c ∈ (a,b) where tangent when drawn is parallel to the X-axis.

a point c ∈ (a,b) where tangent when drawn is parallel to the chord joining end points of the curve y = f(x).

a point c ∈ [a,b] where tangent when drawn is parallel to the X-axis.

yes

no

can't say

may be

c = 7/2

c = 5/2

c = 3/2

c = 9/2

C =  $\frac{\sqrt{5}-2}{3}$  

C = can't be located

c is not defined

Rolle's thm not applicable

 $c=\pm\sqrt{\frac{7}{3}}$  

 $c=\pm\sqrt{\frac{3}{7}}$  

 $c=\sqrt{\frac{7}{3}}$  

 $c=-\sqrt{\frac{3}{7}}$  

c = 6

c =7

c = 5

c = 3