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Determine the derivative of the following function by using the definition of the derivative.
f ( x ) = 2 x2 -16x + 35
Solution
Thus, all we actually have to do is to plug this function into the definition of derivative, (1), and do some algebra. Whereas, admittedly, the algebra will get rather unpleasant at times, but it's just algebra hence don't get excited regarding the fact that now we're computing derivatives.
Firstly plug the function in the definition of the derivative.
Be careful & ensure that you properly deal with parenthesis while doing the subtracting. Multiplying everything and distributing the minus sign through on the second term. Doing this we obtain,
Notice as well that every term into the numerator which didn't have an h in it canceled out and now we can factor an h out of the numerator that will cancel out against the h in the denominator. After that we can calculate the limit.
= 4x-16
hence, the derivative is,
f ′ ( x ) = 4x -16
Special Forms There are a number of nice special forms of some polynomials which can make factoring easier for us on occasion. Following are the special forms. a 2 + 2ab +
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