Suppose that a certain shop has a work of art for sale one day each week. On some weeks the artwork is genuine, while on other weeks the artwork is a shameless forgery! Whenever it's genuine, there is a 20% chance it will be a forgery the next week. Whenever it's a forgery, there is a 24% chance it will be genuine the next week. If the artwork is genuine this week, what is the probability it will be genuine again in three weeks from now

There is a line with slope 1/a going through the point (a, a²). find the equation of the line perpendicular to this line at this point. (don’t let this problem intimidate you! solve the problem as you would if i’d given you specific values. just use variables instead.)

Does the function satisfy the hypotheses of the mean value theorem on the given interval? f(x) = 4x^2 + 3x + 4, [−1, 1] no, f is continuous on [−1, 1] but not differentiable on (−1, 1). no, f is not continuous on [−1, 1]. yes, f is continuous on [−1, 1] and differentiable on (−1, 1) since polynomials are continuous and differentiable on . there is not enough information to verify if this function satisfies the mean value theorem. yes, it does not matter if f is continuous or differentiable; every function satisfies the mean value theorem.

Math i have no idea how to do a and b