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In this lesson, we will learn how to find the slope and equation of the tangent to a curve at a given point.

Q1:

Find the equation of the tangent to the curve π¦ = β 2 π₯ + 8 π₯ β 1 9 3 2 at π₯ = 2 .

Q2:

Find the equation of the tangent to the curve π¦ = 4 π₯ β 6 π₯ + 1 5 3 2 at π₯ = β 1 .

Q3:

Find the equation of the tangent to the curve π¦ = β 2 π₯ β 8 π₯ + 1 7 3 2 at π₯ = β 1 .

Q4:

If the line π¦ = 3 π₯ + 9 is tangent to the graph of the function π at ( 2 , 1 5 ) , what is π β² ( 2 ) ?

Q5:

If the line π¦ = 7 π₯ β 7 is tangent to the graph of the function π at ( 1 , 0 ) , what is π β² ( 1 ) ?

Q6:

What is the π₯ -coordinate of the point where the tangent line to π¦ = π₯ + 1 2 π₯ + 1 1 2 is parallel to the π₯ -axis?

Q7:

What is the π₯ -coordinate of the point where the tangent line to π¦ = π₯ + 9 π₯ + 1 2 2 is parallel to the π₯ -axis?

Q8:

The point ( 3 , 3 ) lies on the curve π¦ = 7 π₯ + π π₯ + π 2 . If the slope of the tangent there is β 1 , what are the values of constants π and π ?

Q9:

The point ( 4 , β 8 ) lies on the curve π¦ = π₯ + π π₯ + π 2 . If the slope of the tangent there is β 2 , what are the values of constants π and π ?

Q10:

Find the equation of the tangent to the curve π¦ = π₯ + 9 π₯ + 2 6 π₯ 3 2 that makes an angle of 1 3 5 β with the positive π₯ -axis.

Q11:

Suppose the line π¦ + 5 π₯ β 1 = 0 touches the curve π ( π₯ ) = π₯ β π₯ + π 2 . What is π ?

Q12:

If the curve π¦ = π π₯ + π π₯ + 2 π₯ + 7 3 2 is tangent to the line π¦ = 7 π₯ β 3 at ( β 1 , β 1 0 ) , find the constants π and π .

Q13:

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

Q14:

The line π₯ β π¦ β 3 = 0 touches the curve π¦ = π π₯ + π π₯ 3 2 at ( 1 , β 2 ) . Find π and π .

Q15:

Do the curves π¦ = β 2 π₯ + 4 π₯ + 2 4 2 and π¦ = β 6 π₯ β 4 π₯ + 2 0 2 have a common tangent at the point of intersection? If so, give the equation of this tangent.

Q16:

Determine the equation of the line tangent to the curve π¦ = 4 π₯ β 2 π₯ + 4 3 2 at point ( β 1 , β 2 ) .

Q17:

The line π¦ + 2 π₯ + π = 0 is tangent to the curve π¦ = π₯ β 1 2 at the point ( π , π ) . Find π , π , and π .

Q18:

The line π¦ = 5 π₯ + 4 is tangent to the graph of function π at the point ( β 1 , β 1 ) . What is π β² ( β 1 ) ?

Q19:

The line 5 π₯ + π¦ = 2 2 touches the curve π¦ = π π₯ + π π₯ β 4 π₯ + 2 3 3 2 at the point ( 1 , 1 7 ) . Find π and π .

Q20:

Find the equation of the tangent to the curve π¦ = π₯ β 2 π₯ 2 at the point ( π₯ , 3 ) on the curve.

Q21:

Find the slope of the tangent to the curve π¦ = β 6 π₯ β 5 π 2 π₯ when π₯ = 1 4 , rounded to the nearest hundredth.

Q22:

Find the equation of the tangent to the curve π¦ = 2 + 2 π₯ β 2 π₯ at the point οΌ 1 , 9 4 ο .

Q23:

Find the equation of the tangent to the curve π¦ = 2 + 2 3 π₯ β π₯ at the point οΌ 1 , 1 7 2 ο .

Q24:

List the equations of all the tangents to π¦ = β π₯ 2 that also lie on the point ( 2 , β 3 ) .

Q25:

List the equations of all the tangents to π¦ = β π₯ 2 that also lie on the point ( 3 , β 8 ) .

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