Verify that the function satisfies the three hypotheses of rolle's theorem on the given interval. then find all numbers c that satisfy the conclusion of rolle's theorem. (enter your answers as a comma-separated list.) f(x) = 1 − 12x + 3x2, [1, 3]

c=2

Step-by-step explanation:

All polynomials are continuous and differentiable on the set of real numbers.

So we just need to confirm on the given interval that f(1)=f(3).

f(1)=1-12(1)+3(1)^2

f(1)=1-12+3

f(1)=-8

f(3)=1-12(3)+3(3)^2

f(3)=1-36+27

f(3)=-8

So this means there is c in (1,3) such that f'(c)=0.

To solve that equation we must differentiate.

f(x)=1-12x+3x^2

f'(x)=0-12+6x

f'(x)=-12+6x

Remember we need yo solve f'(c)=0 for c.

So we need to solve -12+6c=0.

-12+6c=0

Add 12 on both sides:

6c=12

Divide both sides by 6:

c=2

< 6 cm to > 26 cm i believe

step-by-step explanation:

a line is an defined derm because it

a)contains an infinite number of points b) can be used to create other geometric shapes c)describes something that does not have width or depth d) is a term that does not have a formal definition. a line is an undefined term because it: contains an infinite number of points.