How to find the gradient of a secant?

Question

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.

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Answer 1 · 2017-07-20T01:37:43

Your quotient is incorrect.

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

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

For #h != 0# this is the same as #2x+h-2#

The gradient of the secant is #2x+h-2#

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

The derivative is the limit, as #hrarr0# of the gradient of the secant.

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