Part A) Knowledge & Understanding [26 points] Fill in the Blank - *Choose one word or phrase from the box below to complete each sentence correctly. Each word or phrase is only used ONCE!# . difference quotient . differentiable . smooth . power . derivative continuous . differentiation cusp . first principles quotient . tangent . chain 1. (12 points) (a) If you want to quickly find the instantaneous rate of change of a function like y = " at a = 5 just use the rule of differentiation and sub 5 into the derivative function. (b) The derivative is defined as the limit of the (c) If a function has sharp corners, then it is NOT (d) If you use the equation S'(x) = lim /(2 + 4) -/(x) h , to find a derivative function, then you are finding the derivative from (e) If the limit, S'(a) = lim Iath) - f(a) exists at some point ar = a, then the function is at I - Q (f) We can use the rules of to quickly find the derivative of must functions. (g) A function can be both smooth and and yet still have points where it is not differentiable. (h) If we have a function y = /(x), then S'(x), y' and - can all be used to denote the function. (i) The derivative function gives you the slope of the line for all -values in the domain of the function. (j) An edge, peak, or sharp corner on a function is called a (k) The rule lets you differentiate a function like g(x) = (2sin(x) - 1)' without expanding and simplifying first. dy () The following is a statement of the rule: If = P(:E) p'(a)q(a) - p(x)q'(1) . then - [q(x)12

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