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) = 4x2 − 8x + 3, [−1, 3] c =

Rolle's Theorem states that:

If f is a continuous function in [a,b] and is differentiable in (a,b)

such that f(a)=f(b)

Then there exist a constant c in between a and b i.e. c∈[a,b]

such that:  f'(c)=0

Here we have the function f(x) as:

where x∈[-1,3]

Also,

f(-1)=15

(Since,

  )

and f(3)=15

( Since,

)

Hence, there will exist a c∈[-1,3] such that f'(c)=0

Hence, the c that satisfy the conclusion is: c=1

y= 2x+7

changed to y= 5x +7

as slope is increased from 2 to 5

therefore it would be less steeper

so, option d) is correct