Lesson Worksheet: Tangent Lines and Velocity Mathematics

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In this worksheet, we will practice finding the instantaneous rate of change and instantaneous velocity for a function.

Q1:

Evaluate the instantaneous rate of change of 𝑓(𝑥)=2𝑥+9 at 𝑥=−3.

Q2:

Find the slope of the normal to the curve 𝑦=𝑥√8𝑥−5√2𝑥 at the point (2,−2).

  • A7
  • B−72
  • C72
  • D−27
  • E14

Q3:

Evaluate the instantaneous rate of change of 𝑓(𝑥)=7𝑥+9 at 𝑥=𝑥.

  • A7𝑥+14𝑥ℎ+7ℎ+9
  • B14𝑥
  • C7ℎ+14𝑥
  • D7ℎ+14𝑥ℎ

Q4:

Determine the slope of the tangent to the curve of the function 𝑦=(−𝑥+1) when 𝑥=0.

Q5:

The distance 𝑠, in centimeters, is given in terms of time 𝑡, in seconds, by 𝑠=𝑡+𝑡+9. Find the instantaneous rate of change of distance with respect to time at 𝑡=5s.

Q6:

Determine the slope of the tangent to the curve 𝑦=9−2𝑥𝑥−6 at (5,1).

  • A21
  • B−3
  • C3
  • D12
  • E−9

Q7:

Find the slope of the normal to the curve 𝑦=𝑥𝑥−8𝑥𝑥+8𝑥 at 𝑥=−1.

  • A116
  • B−16
  • C−116
  • D16

Q8:

Find the slope of the normal to the curve 𝑦=7𝑥−29𝑥−2 at the point (0,1).

  • A−12
  • B2
  • C−2
  • D12

Q9:

Find the slope of the tangent to the curve 𝑦=9𝑥−9𝑥−8 at the point (1,−8).

Q10:

Find the slope of the tangent to −𝑦=8𝑥−6𝑥+5 at the point where 𝑥=−5.

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