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In this lesson, we will learn how to find the slope of tangents to curves at a given point by understanding the relationship between the derivative and slope of the tangent to a curve.

Q1:

Let Suppose that the tangent to the graph of π at π₯ = 1 makes an angle with the positive π₯ -axis of tangent β 7 . Find π and π .

Q2:

Find the points on the curve π¦ = 3 π₯ β 5 π₯ + 7 3 at which the tangents are parallel to the line 4 π₯ + π¦ β 2 = 0 .

Q3:

Let πΏ be the tangent to the curve π¦ = 4 π₯ + 5 2 at the point ( 1 , 9 ) . Determine the slope of πΏ and the angle it makes with the positive π₯ -axis, giving your answer to the nearest minute.

Q4:

Find the points on the curve π¦ = 3 π₯ + 5 π₯ β 8 3 where the tangent has slope 4.

Q5:

Determine the slope of the tangent to the curve of the function π¦ = ( β π₯ + 1 ) 5 when π₯ = 0 .

Q6:

Find the points on the curve π¦ = ( π₯ β 3 ) οΉ π₯ β 2 ο 2 where the slope of the tangent line is β 2 .

Q7:

Let πΏ be the tangent to the curve π¦ = 7 π₯ + 2 3 at the point ( 1 , 9 ) . Determine the slope of πΏ and the angle it makes with the positive π₯ -axis, giving your answer to the nearest minute.

Q8:

Find the points on π¦ = π₯ β 6 π₯ + 1 0 π₯ + 1 0 3 2 where the tangent is parallel to the line that passes through ( 0 , 5 ) and ( β 6 , β 1 ) .

Q9:

Find the points on the curve π¦ = ( π₯ β 3 ) β 9 2 where the tangent is parallel to the line β 6 π₯ + π¦ β 2 4 = 0 .

Q10:

Find the slope of the tangent to β π¦ = 8 π₯ β 6 π₯ + 5 2 at the point where π₯ = β 5 .

Q11:

Find the slope of the tangent to π¦ = 2 π₯ β 8 π₯ + 5 2 at the point where π₯ = β 5 .

Q12:

Find the slope of the tangent to π¦ = 6 π₯ + 3 π₯ β 8 2 at the point where π₯ = β 2 .

Q13:

At which points are tangents to the curve π¦ = β π₯ β 6 π₯ β 9 π₯ + 9 3 2 parallel to the π₯ -axis?

Q14:

Find the point that lies on the curve π¦ = β π₯ β 8 π₯ β 9 2 , at which the tangent to the curve is perpendicular to the straight line 4 π¦ + π₯ + 7 = 0 .

Q15:

Find the points on the curve π¦ = π₯ β 5 π₯ β 8 3 where the tangent is perpendicular to the line π₯ + 7 π¦ β 9 = 0 .

Q16:

Find the slope of the tangent to the curve π¦ = 9 π₯ β 9 π₯ β 8 3 at the point ( 1 , β 8 ) .

Q17:

Find the slope of the tangent to the curve π¦ = π₯ β 7 π₯ + 1 3 at the point ( 2 , β 5 ) .

Q18:

Find the slope of the tangent to the curve π¦ = 8 π₯ β 4 π₯ + 7 3 at the point ( 1 , 1 1 ) .

Q19:

Find the slope of the tangent to the curve π¦ = 4 π₯ + 4 π₯ 3 at π₯ = 1 .

Q20:

Find the slope of the tangent to the curve π¦ = 4 π₯ β 9 π₯ 3 at π₯ = 2 .

Q21:

Find the slope of the tangent to the curve π¦ = 8 π₯ β π₯ 3 at π₯ = 2 .

Q22:

Find the slope of the tangent to the curve π¦ = 9 π₯ β 6 π₯ 3 at π₯ = β 1 .

Q23:

Differentiate π ( π₯ ) = 3 π₯ + 2 8 , and find the slope of the tangent to its graph at ( 1 , 5 ) .

Q24:

Differentiate π ( π₯ ) = β 5 π₯ + 6 4 , and find the slope of the tangent to its graph at ( β 1 , 1 ) .

Q25:

Differentiate π ( π₯ ) = 4 π₯ + 5 5 , and find the slope of the tangent to its graph at ( β 1 , 1 ) .

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