(a)[1]
Determine the value of $k$. Give your answer correct to $5$ decimal places.
(b)[1]
Determine the gradient of chord $AE$. Give your answer correct to $4$ decimal places.
(c)[1]
Use the table to deduce the value of $f'(2)$.
Mathematics 9709 · AS & A Level · Differentiation
Differentiation — practice question
The curve is defined by $y=f(x)$, where $f(x)=(2x-1)\sqrt{3x-2}-2$. The points below are on the curve. Values that are not exact have been rounded to $5$ decimal places.
$A(2,4)$, $B(2.0001,k)$, $C(2.001,4.00625)$, $D(2.01,4.06261)$, $E(2.1,4.63566)$, $F(3,11.22876)$.
The table gives the gradients of chords $AB$, $AC$, $AD$ and $AF$.