Can Mean Value Theorem be applied to 1 x?

H2 : f is differentiable on the open interval (a,b) . We say that we can apply the Mean Vaue Theorem if both hypotheses are true. [Because the derivative, f'(x)=−1×2 fails to exist at 0 which is in the interval (−1,1) .)]

Does the Mean Value Theorem apply if f/x )= 1 x on [- 1 1?

Consider the function f(x) = |x| on [−1,1]. The Mean Value Theorem does not apply because the derivative is not defined at x = 0.

Can Lagrange’s Mean Value Theorem be applied to?

In the given graph the curve y = f(x) is continuous from x = a and x = b and differentiable within the closed interval [a,b] then according to Lagrange’s mean value theorem, for any function that is continuous on [a, b] and differentiable on (a, b) then there exists some c in the interval (a, b) such that the secant …

Can the Mean Value Theorem be applied to the function?

To apply the Mean Value Theorem the function must be continuous on the closed interval and differentiable on the open interval. This function is a polynomial function, which is both continuous and differentiable on the entire real number line and thus meets these conditions.

How do you prove Lagrange The Mean Value Theorem?

Proof of Lagrange Mean Value Theorem Proof: Let g(x) be the secant line to f(x) passing through the points (a, f(a)) and (b, f(b)). We know that the slope of the secant line is m = f(b)−f(a)b−a f ( b ) − f ( a ) b − a , and the formula for the secant line is y-y1 1 = m (x- x1 1 ).

Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval FX 1x 1 7?

Is it differentiable on the interval (1,7)? Yes, f'(x)=1× exists for all x>0 , so it certainly exists for x∈(1,7) . That’s it. Yes, the function satisfies the hypotheses of the Mean Value Theorem.

Which theorem gives the relation between the value of the function at the point and its first and higher order derivatives?

The Work-Energy Theorem
36.3The Work-Energy Theorem. Here we make a connection between a graph of a function and its derivative and higher order derivatives.

https://www.youtube.com/watch?v=tQy5z12Jeb8