Question

Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = 3x2 − 2x + 1, [0, 2] Yes, it does not matter if f is continuous or differentiable, every function satisfies the Mean Value Theorem. Yes, f is continuous on [0, 2] and differentiable on (0, 2) since polynomials are continuous and differentiable on . No, f is not continuous on [0, 2]. No, f is continuous on [0, 2] but not differentiab

Answer 1

Yes , function is continuous in [0,2] and is differentiable (0,2) since polynomial function are continuous and differentiable

Explanation:

We are given the Function

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

The two basic hypothesis of the mean valued theorem are

• The function should be continuous in [0,2]

• The function should be differentiable in (1,2)

upon checking the condition stated above on the given function

f(x) is continuous in the interval [0,2] as the functions is quadratic and we can conclude that from its graph

also the f(x) is differentiable in (0,2)

f'(x) = 6x - 2

Now the function satisfies both the conditions

so applying MVT

6x-2 = f(2) - f(0) / 2-0

6x-2 = 9 - 1 /2

6x-2 = 4

6x=6

x=1

so this is the tangent line for this given function.