# Worksheet: Tangents to the Graph of a Function

Q1:

Find the equation of the tangent to the curve at .

• A
• B
• C
• D

Q2:

Find the equation of the tangent to the curve at .

• A
• B
• C
• D

Q3:

Find the equation of the tangent to the curve at .

• A
• B
• C
• D

Q4:

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

Q5:

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

Q6:

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

• A
• B6
• C0
• D

Q7:

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

• A
• B
• C0
• D

Q8:

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

• A ,
• B ,
• C ,
• D ,

Q9:

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

• A ,
• B ,
• C ,
• D ,

Q10:

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

• A
• B
• C
• D

Q11:

Suppose the line touches the curve . What is ?

Q12:

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

• A ,
• B ,
• C ,
• D ,

Q13:

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

• A
• B
• C
• D

Q14:

The line touches the curve at . Find and .

• A ,
• B ,
• C ,
• D ,

Q15:

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

• Ayes,
• Byes,
• Cno
• Dyes,

Q16:

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

• A
• B
• C
• D
• E

Q17:

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

• A , ,
• B , ,
• C , ,
• D , ,

Q18:

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

Q19:

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

• A ,
• B ,
• C ,
• D ,

Q20:

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

• A ,
• B ,
• C ,
• D ,

Q21:

Find the gradient of the tangent to the curve when , approximated to the nearest hundredth, if needed.

• A
• B
• C18.94
• D

Q22:

Find 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 .

• A
• B
• C
• D

Q24:

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

• A ,
• B ,
• C ,
• D ,

Q25:

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

• A ,
• B ,
• C ,
• D ,