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- If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?Which of the following statements is false for a function f that can be differentiated at least twice? a) If f ′ (c) = 0 and the sign of the derivative function f ′ (x) at point c changes from "+" to "-", point c is definitely the local maximum point of the function. b) If f ′ (c) = f ′ ′ (c) = 0, point (c, f (c)) is definitely the inflection point of the function graph. c) If f ′ (c) = 0 and f ′ ′ (c)> 0, point c is definitely the local minimum point of the function. d) If f ′ (c) = 0 and f ′ ′ (c) <0, point c is definitely the local maximum point of the function. e) If f ′ (c) = 0 and the sign of the derivative function f ′ (x) at point c changes from "-" to "+", point c is definitely the local minimum point of the function. f) noneFor what value of the constant c is the function f continuouson (∞,-∞)?
- If the function is defined y=2x when x<=3 and y=-x+9 when x>=3, is this function differentiable at x=3? Also, is this function continuous at x=3?4. Determine whether or not the following functions are uniformly continuous.(Use ε and δ to prove your work through e delta definition) Kindly do only a,b and c but do ASAPProve that the given function is not differentiable at (-1,0).
- Q3:Verify the third hypothesis of Rolle’s Theorem for the function on the interval f(x)=x^2[SQRT(25-X)] on the interval [0, 25] then find all values of c guaranteed by Rolle’sTheorem.Suppose that u(x) is a differentiable function suchthatOver which intervals does the function f have negative concavity (concave down)?