# 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 -coordinate of the point where the tangent line to is parallel to the -axis?

• A
• B0
• C6
• D

Q4:

The point lies on the curve . If the slope of the tangent there is , what are the values of constants and ?

• A ,
• B ,
• C ,
• D ,

Q5:

Find the point on the curve at which the tangent to the curve is parallel to the -axis.

• A
• B
• C
• D

Q6:

List the equations of all the tangents to that also lie on the point .

• A ,
• B ,
• C ,
• D ,

Q7:

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

• A
• B
• C
• D

Q8:

Suppose the line touches the curve . What is ?

Q9:

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

• A ,
• B ,
• C ,
• D ,

Q10:

The line touches the curve at . Find and .

• A ,
• B ,
• C ,
• D ,

Q11:

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,

Q12:

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

• A
• B
• C
• D
• E

Q13:

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

• A , ,
• B , ,
• C , ,
• D , ,

Q14:

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

Q15:

The line touches the curve at the point . Find and .

• A ,
• B ,
• C ,
• D ,

Q16:

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

• A ,
• B ,
• C ,
• D ,

Q17:

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

• A
• B
• C
• D

Q18:

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

• A ,
• B ,
• C ,
• D ,

Q19:

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

• A
• B
• C
• D
• E

Q20:

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

• A
• B
• C
• D

Q21:

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

• A ,
• B ,
• C ,
• D ,

Q22:

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

• A
• B
• C
• D

Q23:

Find the equation of the tangent to the curve at the point with -coordinate 0.

• A
• B
• C
• D

Q24:

Find the equation of the tangent to the curve at .

• A
• B
• C
• D

Q25:

Find the equation of the normal to the curve at .

• A
• B
• C
• D