(1) (a) State the definition of the derivative of a function f at a point a....

 

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(1) (a) State the definition of the derivative of a function f at a point a. Note: parts (b) and (c) must be solved directly using this definition. Just applying the power rule or similar formulas for derivatives will not result in marks. (b) Directly from the definition, calculate the derivative of the function f(x) = x at the point x = 2. (c) Directly from the definition, calculate the derivative of the function g(x) = 1- at the point x = 3. (d) Use the Intermediate Value Theorem to show that there is a number a in the interval - (1) (a) State the definition of the derivative of a function f at a point a. Note: parts (b) and (c) must be solved directly using this definition. Just applying the power rule or similar formulas for derivatives will not result in marks. (b) Directly from the definition, calculate the derivative of the function f(x) = x at the point x = 2. (c) Directly from the definition, calculate the derivative of the function g(x) = 1- at the point x = 3. (d) Use the Intermediate Value Theorem to show that there is a number a in the interval -