In this lesson, we will learn how to calculate the derivative of a polynomial function using the formal definition of the derivative as a limiting process.

Q1:

Let . Use the definition of derivative to determine . What is the gradient of the tangent to its graph at ?

Q2:

Q3:

Q4:

Q5:

Find the derivative of the function π ( π₯ ) = 6 π₯ β 7 π₯ 3 2 using the definition of derivative, and then state the domain of the function and the domain of its derivative.

Q6:

Find the derivative of the function π ( π₯ ) = β 8 π₯ + 9 π₯ 3 2 using the definition of derivative, and then state the domain of the function and the domain of its derivative.

Q7:

Find the derivative of the function π ( π₯ ) = 2 π₯ β 3 π₯ 3 2 using the definition of derivative, and then state the domain of the function and the domain of its derivative.

Q8:

Q9:

Let π ( π₯ ) = β 6 β π₯ β 6 . Use the definition of the derivative to determine π β² ( π₯ ) .

Q10:

Determine the derivative of the function π ( π₯ ) = β 2 π₯ β 1 6 using the definition of the derivative.

Q11:

Evaluate l i m β β 0 π ( β + 1 2 ) β π ( β β 1 7 ) + π ( β 1 7 ) β π ( 1 2 ) β .

Q12:

Evaluate l i m β β 0 π ( β + 4 ) β π ( β β 2 ) + π ( β 2 ) β π ( 4 ) β .

Q13:

Given a function with π ( β 3 ) = 7 and π β² ( β 3 ) = 3 , what is l i m β β 0 5 β π ( β β 3 ) β 7 ?

Q14:

Consider a function with π ( β 8 ) = 3 and π β² ( β 8 ) = 7 . What is l i m π₯ β β 8 π ( π₯ ) ?

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