The graph of a function f(x) is shown below. For what values of x is f(x) not differentiable? Differentiate the function: 6 f(x) = x10 + 7x10 Answer: f'(x) = Check x = (smallest value) * = largest value) In this question we will use the definition of the derivative to calculate the derivative of f (x) = - By definition, f'(x) is given by the limit of the difference quotient: f'(x) = lim f(x + h) - f(x) h-0 h Substituting our particular choice of function f(x), this limit becomes: f'(x) = lim h - 0 After performing algebraic manipulations and simplifying, we can evaluate the limit to determine f'(x). The result is: f' (x) =