Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = 4x2 − 3x + 2, [0, 2] Yes, it do
es not matter if f is continuous or differentiable, every function satifies the Mean Value Theorem. Yes, f is continuous on [0, 2] and differentiable on (0, 2) since polynomials are continuous and differentiable on double-struck R. No, f is not continuous on [0, 2]. No, f is continuous on [0, 2] but not differentiable on (0, 2). There is not enough information to verify if this function satifies the Mean Value Theorem. Correct: Your answer is correct. If it satisfies the hypotheses, find all numbers c that satisfy the conclusion of the Mean Value Theorem. (Enter your answers as a comma-separated list. If it does not satisify the hypotheses, enter DNE). c =
where f'(c) is the derivative of the function: 8x - 3;
f(b) is the function evaluated at an x value of 2 (the second number in the interval): f(b) = 12;
f(a) is the function evaluated at an x value of 1 (the first number in the interval: f(a) = 2
Setting up:
So basically what we end up with is
8c - 3 = 5 and
8c = 8 so
c = 1
This function does in fact satisfy the requirements for the MVT: it is continuous on the interval and it is differentiable on the interval as polynomials by nature are continuous and differentiable on all values of x.
we know that The inscribed angle measures half of the arc it comprises so ∠ GHL=(1/2)*[arc LI] ∠ GHL=32° 32°=(1/2)*arc LI arc LI=32°*2-------> arc LI=64°