Find the average gradient between the points (t;f(t)) and (t+h;f(t+h)) on the curve f(x)=x^2.

Expert Answers

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We have the function f(x) = x^2.

The points given to us are (t , f(t)) and (t+h , f(t+h))

or (t , t^2) and ((t + h) , (t + h)^2)

The gradient between these points is

=>[ (t + h)^2 - t^2] / [ t + h - t]

=> (t + h - t)(t + h + t) / h

=> 2t + h

The required gradient is 2t + h

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