In this worksheet, we will practice finding the slope and equation of the tangent and normal to a curve at a given point using derivatives.
Q1:
Find the equation of the tangent to the curve π¦=β2π₯+8π₯β19ο©ο¨ at π₯=2.
Q2:
Find the equation of the normal to the curve π¦=β2π₯β7π₯+2ο©ο¨ at π₯=β2.
Q3:
What is the π₯-coordinate of the point where the tangent line to π¦=π₯+12π₯+11ο¨ is parallel to the π₯-axis?
Q4:
Find the equation of the tangent to the curve π¦=π₯+9π₯+26π₯ο©ο¨ that makes an angle of 135β with the positive π₯-axis.
Q5:
Find all points with π₯-coordinates in [0,π) where the curve π¦=2π₯sin has a tangent that is parallel to the line π¦=βπ₯β18.
Q6:
Find the equations to the tangent lines of the curve π¦=(π₯+8)(π₯+10) at the points where this curve intersects the π₯-axis.
Q7:
Find the equation of the tangent to the curve π(π₯)=π₯ο¨ at its point of intersection with the curve π(π₯)=125π₯.
Q8:
Find the equation of the normal to the curve π¦=5π₯+93π₯β5 at (1,β7).
Q9:
Find the points on the curve π¦=3π₯β5π₯+7ο© at which the tangents are parallel to the line 4π₯+π¦β2=0.
Q10:
The curves π¦=2π₯β3π₯β2ο¨ and π¦=β3π₯+5π₯β5ο¨ intersect orthogonally at a point. What is this point?
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