Each of the following statements is false. Provide why the statement is false.

Question

1) Every function that is continuous at x=a is differentiable at x=a.

2) The tangent line to y=f(x) when x=x0 is given by y=fprime(x0)x+f(x0).

3) The linerization of a function f(x) when x=x0 is the value of the derivative of the function when x=x0.

4) If x=f^-1 (y) (meaning y= f(x)), then (dy/dx) = -(f(y))^-2 fprime(y)

Answer 1

1) Every function that is continuous at x=a is differentiable at x=a.

Look at f(x) = |x|