Determine if the statement is true or false. Provide a counterexample or proof.  Suppose f is a continuous injective function, and f-1 is differentiable, then f is also differentiable.

Q: List x-coordinates of all points at which the function is not differentiable. Justify jour answers!

A: A function fx is not differentiable at any point for two cases, 1) fx is not continuous at point. 2)…

Q: Consider two functions, f and g, on the interval (-10, 10). Their graphs are depicted below:…

A: The condition of a function f(x) continuity at x=a

Q: 4). t(x)= x + 2oSX ,[0, 2T]

A: We can use application of derivative in order to solve the given problem.

Q: Find the values of a and b that make f continuous everywhere. b = f(x): x-2 ax² - 6x + 3 4x -a + b…

A:

Q: Use the graph of f to find the interval(s) on which f is decreasing., Where applicable, use interval…

A: we have to use the graph to identify where f(x) is decreasing.

Q: Let f be a function of x. Which of the following statements, if true, would guarantee that there is…

A:

Q: For questions 10-11, let f(x) = One can see that f'(x) = 2x and %3D (x-1)2 (x-1)3 (x) = 2(2x+1)…

A:

Q: Determine whether the function f(x) = x2 from the set of integers to the set of integers is…

A:

Q: Tell if the piece-wise function is continuous on the given interval. Put a CHECK MARK AFTER the…

A: Given graph,

Q: 20 for x 5 Let f be the function defined above. Which of the following statements is true? A) f is…

A: Here, we are given the following function. Now,          limx→5-f(x)=limx→5-(x2-20)…

Q: Determine the values of x where the function f (æ) is not continuous. Label each discontinuity as…

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: