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differentiation help

points P1, (1,y1), P2 (1.01, y2, and P3 (1.1, y3) lie on the curve y=k^2. the gradient of the chord P1P3 is 6.3 and the gradient of the chord P1P2 is 6.03.

1)what do these results suggest about the gradient of the tangent to the curve y=kx^2 at P1?

is this just that 6.3>gradient>6.03??

2)deduce the value of k
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Notnek
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Original post by eyenarbi
points P1, (1,y1), P2 (1.01, y2, and P3 (1.1, y3) lie on the curve y=k^2. the gradient of the chord P1P3 is 6.3 and the gradient of the chord P1P2 is 6.03.

1)what do these results suggest about the gradient of the tangent to the curve y=kx^2 at P1?

is this just that 6.3>gradient>6.03??

2)deduce the value of k

1) That's not right. Look at this diagram:



Using the letters from your question, point P1 = A, P2 = C and P3 = B. What can you say about the gradient of the tangent compared to the gradients of the chords P1P2 and P1P3 (AC and AB)?

2) Start by writing the coordinates in terms of k. E.g. when x = 1, y = kx^2 = k

so the coordinate (1,y1) can be written as (1, k).

Carry on from there and post all your working if you get stuck.

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