MA 181 Written Assignment 4 Due: Wednesday, Feb. 19th at the beginning of class Be sure to written neatly and clearly on another sheet of paper. This is not a worksheet. Always show your work and...

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MA 181 Written Assignment 4 Due: Wednesday, Feb. 19th at the beginning of class Be sure to written neatly and clearly on another sheet of paper. This is not a worksheet. Always show your work and justify your answers. Unstapled homework will not be accepted. 1. Use the limit definition of the derivative of a function to show, d dx [cf(x)] = cf ′(x) where c is a constant and f(x) is a differentiable function. 2. Use the rules of differentiation to find the derivative of the following functions: (a) y = x + 3 x2 + 9 (b) f(x) = 4x5 − 2x4 − 3x3 + 5x2 − 87x + 2020 (c) h(t) = t7 − ( 3 √ t)5 (d) y = (x4 + x3 + 7x)(ex + 67) (e) g(u) = x 2−9 x+ex 3. Find the tangent line to the graph of the function f(x) = 3 √ x at x = 8. 1