How to find the gradient of a secant?

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Can someone please help me with question 3? I know how to work out the gradient and got -2xh-h^2+h/-h but the answer says 2x-2.

1 Answer
Jul 20, 2017

Your quotient is incorrect.

Explanation:

It should be (-2xh-h^2+2h)/(-h)2xhh2+2hh

Which is the same as (-h(2x+h-2))/(-h).h(2x+h2)h.

For h != 0h0 this is the same as 2x+h-22x+h2

The gradient of the secant is 2x+h-22x+h2

To finish the question, you need to find the derivative.

The derivative is the limit, as hrarr0h0 of the gradient of the secant.

lim_(hrarr0)(2x+h-2) = 2x-2 as your answer says.