1. Consider the graphs of the continuous functions y=f(x) and y=g(x) below. Numerically simplify your answers. (a) (2) D

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1 Consider The Graphs Of The Continuous Functions Y F X And Y G X Below Numerically Simplify Your Answers A 2 D 1 (46.35 KiB) Viewed 35 times

1. Consider the graphs of the continuous functions y=f(x) and y=g(x) below. Numerically simplify your answers. (a) (2) Determine the value(s) of x where g(x) in non-differentiable. (b) (2) Let u(x)=5f(x)+3g(x). Compute u′(4). (c) (2) Let v(x)=x2g(x)​, Compute v′(4). (d) (2) Let w(x)=f(f(x)). Compute w′(4). 2. Determine an unsimplified version of f′(x) without the help of Mathematica. You must write the names of more than 50%1 of the "Differentiation Rules" for each problem below that you used. (a) (4) f(x)=(x2+3x−6)⋅(x3−x+3) (b) (4) f(x)=1+x2sin(x)​ (c) (4) f(x)=3x3+2x2​+xπ+56. 3. Suppose f(x)=2x3+3x2−12x+7. (a) (4) Determine the equation of the tangent line at x=2 for the graph of y=f(x). (b) (4) Determine the value(s) of x for which the tangent line is horizontal for the graph of y=f(x). 4. (6) Consider the graph given by x2−3xy+y2+5=0. Determine the equation of the tangent line at the point (3,2). 5. (4) Sketch a graph of a function that has a jump discontinuity at x=3 which is also right continuous at x=3. 6. Suppose that f(5)=2,f′(5)=5,g(5)=−3 and g′(5)=5. Suppose u(x)=f(x)g(x) and v(x)=g(x)f(x)​. Determine the following values. (a) (4) u′(5) (b) (4) v′(5)