# Worksheet: Slope of a Polar Curve

In this worksheet, we will practice finding the derivatives of polar curves and the slope of a polar curve.

Q1:

Find the slope of the tangent line to the curve at .

• A
• B
• C0
• D
• E

Q2:

Find the slope of the tangent line to the polar curve at the point .

• A
• B0
• C
• D

Q3:

Find the slope of the tangent line to the curve at .

• A
• B
• C
• D
• E

Q4:

Find the slope of the tangent line to the curve at .

• A
• B
• C
• D
• E

Q5:

Find the slope of the tangent line to the curve at .

• A
• B0
• C
• D
• E

Q6:

Find the slope of the tangent line to the curve at .

• A
• B
• C
• D
• E

Q7:

Find the slope of the tangent line to the polar curve at the point .

• A
• B
• C
• D
• E

Q8:

Find the slope of the tangent line to the curve at .

• A
• B
• C
• D
• E

Q9:

Find the slope of the tangent line to at . Round your answer to 3 decimal places.

Q10:

Find the slope of a tangent line to at .

• A4
• B0
• C−1
• D1
• EThe slope is undefined at .

Q11:

Find the slope of a tangent line to at .

• A
• B
• C
• D
• E

Q12:

Find the slope of a tangent line to at .

Q13:

Find the slope of the tangent line to at the point .

Q14:

Find the slope of the tangent line to at . Give your answer to 3 decimal places.

Q15:

For the cardioid , find the slope of the tangent line at .

Q16:

Find the points at which has a horizontal or vertical tangent line.

• AHorizontal tangents at and , vertical tangents at and
• BHorizontal tangents at and , vertical tangents at and
• CNo horizontal tangents, vertical tangents at and
• DHorizontal tangents at , no vertical tangents
• EHorizontal tangents at and , vertical tangents at and

Q17:

Given a polar curve defined by , form an expression for the slope of the curve in terms of and .

• A
• B
• C
• D
• E

Q18:

Find the slope of the tangent line to at .

• A
• B1
• CThe slope of the tangent line is undefined.
• D
• E

Q19:

Find the slope of the tangent line to at the point .

• A
• B
• C
• D0
• E

Q20:

Find the slopes of the tangent lines to at the tips of the leaves.

• AThe slope is at , at , and 0 at .
• BThe slope is at , at , and undefined at .
• CThe slope is at , at , and 0 at .
• DThe slope is at , at , and 0 at .
• EThe slope is 0 at the tips of all the leaves.

Q21:

Find the slopes of the tangent lines to at the tips of the leaves.

• AThe slope is 0 at the tips of all the leaves.
• BThe slope is 0 at and and the slope is undefined at and .
• CThe slope is undefined at and and the slope is 0 at and .
• DThe slope is 1 at and and the slope is at and .
• EThe slope is undefined at the tips of all the leaves.

Q22:

Find the slope of the tangent line to the curve at .

• A
• B
• C0
• D
• E

Q23:

Find the slope of the tangent line to the polar curve at the point .

• A
• B
• C
• D
• E

Q24:

Find the slope of the tangent line to the curve at .

• A
• B1
• C
• D

Q25:

Find the slope of the tangent line to the curve at .

• A2
• B
• C
• D1
• E