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Derivatives and Their Applications · Paper 2 — Free Maths AI SL Practice Questions

1MasterySAQ-SDefinition of a derivative (rate of change)6 marksPaper 2~9 min

The graph of the function

f(x) = -0.5x^2 + 3x + 1

is shown below for

0 \leq x \leq 6

(a)

Calculate the gradient of the chord

AB

. [2 marks]

(b)

Calculate the gradient of the tangent to the curve at

x = 1

. [2 marks]

(c)

The Mean Value Theorem guarantees a point

C

on the curve between

A

and

B

where the tangent is parallel to chord

AB

. Find the coordinates of

C

and explain why

C

lies strictly between

A

and

B

. [2 marks]

Solutions

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