Mathematics

Problem

Point

P(4, 2)

lies on the curve with equation

y = \sqrt{x}

. The table shows the coordinates of a variable point

Q

and the gradient of the chord

PQ

. Complete the table and use it to estimate the gradient of the curve at

P

$x_Q$	$y_Q$	$\Delta x$	$\Delta y$	Gradient of $PQ$
5	2.236	1	0.236	0.236
4.1	2.025	0.1
4.01
4.001