Explain in your own words (1). The definition of the derivative of a function f(x) at a point (x1...
Using the definition of the derivative, find f'(x) for the following function. 3. f(x) = x2 + x - 1 the definition of the derivative f'(x) = lim f(x+h)-f(x) h h-0 What is the slope of tangent line to this curve at x = -1?
Answer any two from questions (1) throun) (23 point (1) Find the derivative of f(x)=2e3*then explain why f(x)=2e3* can only have a tangent with a positive slope. +5x2 - 9x -12 at the point (2,-2). (2) Find the equation for a line that is tangent to f(x) = x
1. For each function below find a formula for the nth derivative of f(x) evaluated at -a. In other words, find f (a). Then use your formula to find the associated Taylor Series for each of the functions at the given center (a) () for a 3 (b) f(x)-e for a - 1 2. Find the associated Taylor Series for the function f(x) = sin x with center a =-, as well as the radius (not interval) of convergence. You...