# Worksheet: Tangents to the Graph of a Function

In this worksheet, we will practice finding the slope and equation of the tangent to a curve at a given point using derivatives.

Q1:

Find the equation of the tangent to the curve at .

• A
• B
• C
• D

Q2:

If the line is tangent to the graph of the function at , what is ?

Q3:

What is the of the point where the tangent line to is parallel to the ?

• A
• B0
• C6
• D

Q4:

Find the equation of the tangent to the curve that makes an angle of with the positive -axis.

• A
• B
• C
• D

Q5:

If the curve is tangent to the line at , find the constants and .

• A,
• B,
• C,
• D,

Q6:

The line touches the curve at . Find and .

• A,
• B,
• C,
• D,

Q7:

Do the curves and have a common tangent at the point of intersection? If so, give the equation of this tangent.

• ANo
• BYes,
• CYes,
• DYes,

Q8:

Determine the equation of the line tangent to the curve at point .

• A
• B
• C
• D
• E

Q9:

The line is tangent to the curve at the point . Find , , and .

• A, ,
• B, ,
• C, ,
• D, ,

Q10:

The line is tangent to the graph of function at the point . What is ?

Q11:

Find the equation of the tangent to the curve at the point on the curve.

• A,
• B,
• C,
• D,

Q12:

List the equations of the normals to at the points where this curve meets the line .

• A,
• B,
• C,
• D,

Q13:

Determine the equation of the line normal to the curve at the point .

• A
• B
• C
• D
• E

Q14:

Determine the equation of the common tangent to the two curves and .

• A
• B
• C
• D

Q15:

Find the equations to the tangent lines of the curve at the points where this curve intersects the -axis.

• A,
• B,
• C,
• D,

Q16:

Find the equation of the normal to the curve at .

• A
• B
• C
• D

Q17:

Find the equations of the two tangents to the curve that are perpendicular to the line .

• A,
• B,
• C,
• D,

Q18:

Find the equation of the normal to the curve at .

• A
• B
• C
• D

Q19:

Two tangents to are parallel. Given that one tangent is at , find the equation of the other one.

• A
• B
• C
• D

Q20:

Find the equations of the tangents to the curve that are parallel to the straight line .

• A,
• B,
• C,
• D,

Q21:

Find the equation of the normal to the curve at .

• A
• B
• C
• D

Q22:

Find the equation of the tangent to the curve at its point of intersection with the curve .

• A
• B
• C
• D

Q23:

Determine the equation of the tangent to the curve at point .

• A
• B
• C
• D
• E

Q24:

Find the equation of the tangent to the curve at .

• A
• B
• C
• D
• E

Q25:

Find the equation of the tangent to the curve at .

• A
• B
• C
• D