Worksheet: Variation Functions

In this worksheet, we will practice evaluating the variation function at a point for a given function.

Q1:

Determine the variation function 𝑉() for 𝑓(𝑥)=𝑎𝑥+𝑏𝑥+2 at 𝑥=1, and, from 𝑉12=72 and 𝑓(1)=6, determine the constants 𝑎 and 𝑏.

  • A𝑉()=2𝑎𝑏, 𝑎=2, 𝑏=2
  • B𝑉()=𝑎(+2)+𝑏, 𝑎=2, 𝑏=2
  • C𝑉()=𝑎+(2𝑎+𝑏), 𝑎=2, 𝑏=2
  • D𝑉()=𝑎(+2)𝑏, 𝑎=2, 𝑏=2

Q2:

Determine the variation function 𝑉() for 𝑓(𝑥)=4𝑥9𝑥+9 at 𝑥=1.

  • A𝑉()=4
  • B𝑉()=4+28
  • C𝑉()=4+
  • D𝑉()=41
  • E𝑉()=4+

Q3:

If 𝑉 is the variation function for 𝑓(𝑥)=𝑥4𝑥+2, what is 𝑉(0.2) when 𝑥=8?

Q4:

Determine the variation function 𝑉() for 𝑓(𝑥)=𝑥+𝑎𝑥+17 at 𝑥=1. Additionally, find 𝑎 if 𝑉49=116.

  • A𝑉()=+2+𝑎𝑎=0.61,
  • B𝑉()=+(2+𝑎)𝑎=2.57,
  • C𝑉()=+2+𝑎𝑎=0.28,
  • D𝑉()=+(2+𝑎)+34𝑎=31.43,

Q5:

Determine the variation function 𝑉() for 𝑓(𝑥)=8𝑥5𝑥8 at 𝑥=1.

  • A𝑉()=811
  • B𝑉()=8+1122
  • C𝑉()=811
  • D𝑉()=8+11
  • E𝑉()=8+11

Q6:

Determine the variation of the function 𝑓(𝑥)=𝑒 at 𝑥=2.

  • A𝑉()=𝑒
  • B𝑉()=𝑒
  • C𝑉()=𝑒1
  • D𝑉()=𝑒1𝑒
  • E𝑉()=𝑒𝑒1

Q7:

Determine the variation function of 𝑓(𝑥)=𝑎𝑥sin at 𝑥=𝜋.

  • A𝑉()=𝑎sin
  • B𝑉()=𝑎+sin
  • C𝑉()=𝑎sin
  • D𝑉()=𝑎cos
  • E𝑉()=𝑎cos

If 𝑉𝜋2=1, find 𝑎.

Q8:

Determine the variation function of 𝑓(𝑥)=𝑥cos at 𝑥=𝜋2.

  • A𝑉()=()sin
  • B𝑉()=()cos
  • C𝑉()=()sin
  • D𝑉()=()cos
  • E𝑉()=+𝜋2sin

Q9:

Determine the variation of the function 𝑓(𝑥)=𝑎𝑥+2𝑥 at 𝑥=1.

  • A𝑉()=𝑎+(2𝑎2)
  • B𝑉()=𝑎+(2𝑎+2)
  • C𝑉()=𝑎+(𝑎+2)
  • D𝑉()=𝑎+2

If 𝑉(1)=5, find 𝑎.

  • A1
  • B1
  • C2
  • D2
  • E0

Q10:

If the variation function of 𝑓(𝑥)=𝑎𝑥+𝑏𝑥 at 𝑥=𝑑 is 𝑉()=𝑎+𝑏, what is the value of 𝑑?

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