Question

Each of the following statements is false. Provide why the statement is false.
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)
you must have some ideas on these. Surely you have read the definition of differentiable. It's late, so I'll have to get back to you, but in the meantime, what are your thoughts? I'm sure your text explains these ideas, and I know google can help.

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