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In this lesson, we will learn how to evaluate the rate of change of a function at a point.

Q1:

What is the rate of change for the function π¦ = β 5 π₯ β 9 ?

Q2:

If the function π ( π₯ ) = 1 1 π₯ + 1 6 3 , find the rate-of-change function when π₯ = π₯ 1 .

Q3:

The biomass of a bacterial culture in milligrams as a function of time in minutes is given by π ( π‘ ) = 7 1 π‘ + 6 3 ο© . What is the rate of growth of the culture when π‘ = 2 m i n u t e s ?

Q4:

The distance in metres travelled by a body in π‘ seconds is π = 9 π‘ + 5 π‘ + 7 2 . What is the rate of change of π with respect to π‘ when π‘ = 1 1 ?

Q5:

A particle moves along the curve π¦ = 3 π₯ β 2 π₯ β 6 2 . At what point is the rate of change in its π¦ -coordinate four times the rate of change of its π₯ -coordinate?

Q6:

Find the rate of change of the slope of the tangent of function π ( π₯ ) = β π₯ 3 at π₯ = 8 .

Q7:

The output in mg of a chemical reaction after π‘ seconds is given by π¦ = 4 π‘ 3 . What is the rate of production of this reaction at π‘ = 2 seconds?

Q8:

Let π ( π₯ ) = 5 + π π₯ + π π₯ 2 . Suppose that the change in π ( π₯ ) as π₯ goes from β 1 to 2 is 6 and that the rate of change of π ( π₯ ) at π₯ = 2 is 17. Determine π and π .

Q9:

Find the rate of change of π ( π₯ ) = 5 π₯ + 1 7 3 when π₯ = 3 .

Q10:

Determine the rate of change of the function π ( π₯ ) = π₯ + 4 8 π₯ + 3 when π₯ = π₯ 1 .

Q11:

Evaluate the rate of change of π ( π₯ ) = 6 π₯ + 7 7 π₯ 2 at π₯ = 3 .

Q12:

If the function π ( π₯ ) = 5 π₯ β 1 8 3 , find the rate-of-change function when π₯ = π₯ 1 .

Q13:

The biomass of a bacterial culture in milligrams as a function of time in minutes is given by π ( π‘ ) = 5 7 π‘ + 1 7 ο© . What is the rate of growth of the culture when π‘ = 2 m i n u t e s ?

Q14:

The distance in metres travelled by a body in π‘ seconds is π = 7 π‘ + 6 π‘ + 5 2 . What is the rate of change of π with respect to π‘ when π‘ = 1 5 ?

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