ASK YOUR TEACHER Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = x3 + x − 9, [0, 2]

Yes

Step-by-step explanation:

The Mean Value Theorem states that if f(x) is defined and continuous on the interval [a,b] and differentiable on (a,b), then there is at least one number c in the interval (a,b) (that is a < c < b) such that

Given

f(x) is defined, continuous and differentiable.

Therefore:

Since c is in the given interval, the function satisfy the hypotheses of the Mean Value Theorem on the given interval.

parallel and congruent

step-by-step explanation:

the movement of translation is linear.   these have the same translation because you are using the same rule for each point of the triangle so you will see the same slope being used to get from a point on the triangle to its image.

same slope!   you should think parallel when you see those 2 word together (well unless it's the same line but it can't be because we are coming from different points here)

congruent! because each point is being moved the same distance.