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Basic Differentiation Rules and Rates of Change

Please help me with problems No. 18, 36, 42, 44, 48, 50, 56.

Please see attached file.

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Q18: f(x) = 2x^3 - x^2 +3x
The derivative is f'(x)=6x^2-2x+3

Q36: The slope of the graph of the function means find the derivative!
f(x)=3(5-x)^2
f'(x) = 3.2 (5-x)^1. (-1) the -1 is the derivative of 5-x (the inside function).
f'(x) = -6 (5-x) or -30 +6x

[ If you don't use this rule you can also just expand the brackets, simplify, then find derivative, as in 3(5-x)^2=3(25-10x+x^2)=75 - 30x + 3x^2 and the ...

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Basic derivatives rules and rates of change are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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