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

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

The graph of

y = f(x)

for

-2 \leq x \leq 4

is shown below. A tangent line is drawn to the curve at point

P

where

x = 1

. The tangent line passes through the points

(-1, 1)

and

(3, 5)

(a)

Calculate the gradient of the tangent line at

P

. [2 marks]

(b)

The tangent line at

P

has equation

y = x + 2

. Determine the

x

-coordinate of the point where this tangent line intersects the line

y = 3x - 4

. [2 marks]

(c)

Calculate the average rate of change of

f

between

x = -2

and

x = 4

. Give your answer as an exact fraction. [2 marks]

Solutions

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