For the curve y=x2 - 4, the tangent gradient at x=a is 2a. Calculate delta y and the average gradien

Question

For the curve y=x2 - 4, the tangent gradient at x=a is 2a. Calculate delta y and the average gradient when x changes from 3 to 2910. Compare this average with the tangent gradient at the original point, and describe what the average approaches as delta x 0.

Accepted Answer

$\delta y=- \dfrac{59}{100},\quad\dfrac{\delta y}{\delta x}=\dfrac{59}{10}$. The average tends to $6$.

Average and instantaneous gradients

Average and instantaneous gradients

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