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.
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 , ,
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 ,
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
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