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A major quiz for ma140-09, focusing on explaining why a function has a root in a specific interval, finding derivatives using the definition, and determining the equation of the tangent line. It also includes questions on finding the derivative without using product or quotient rules, and finding a second-degree polynomial given certain conditions.
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2/11/
Major Quiz 2 _________________, come on down!
Show all your work and explain your answers completely. I cannot give partial credit for answers that are both wrong and unexplained. Even correct "bottom line" answers that are mysterious and unsupported will not be considered completely correct. Show me what you are thinking. Try to keep your answers neat and organized so that I can follow them easily.
1.) Explain why f(x) has a root in the interval [0,1] where f ( ) x = 2 x^5 + 3 x − 1.
2.) Using the definition of the derivative, find f '( ) x where f ( ) x = x + 2.
3.) Find and equation of the line tangent to the graph of y = 4x^2 – 3x + 1 when x = -1.
2/11/
4.) Determine f '( ) x in each of the following. In part a, you are not allowed to use the product or quotient rules.
(a)
2
3
(c)
3 4
5.) Find h '(2)if h x ( ) = ( f ⋅ g )( ) x , if f (2) = 6, g (2) = 7, f '(2) = −3, g '(2) = 8.