The equation of a curve is y = 3x² -4x + 1, Find the gradient function of the curve and its value when x = 2

The equation of a curve is
y = 3x² -4x + 1
a) Find the gradient function of the curve and its value when x = 2
b) Determine the equation of the tangent to the curve at(2,5)

Answers

a) Given y = 3x² - 4x + 1

Gradient function is

$\frac{dy}{dx}$ = 6x - 4

Its value when x = 2 is 6 x 2 - 4 = 12 - 4 = 8

b) i) Equation of the tangent to the curve

at (2,5)

Take points (2,5)

and (x,y) whose gradient is 8

therefore $\frac{y - \;5}{x-\;2}$ = 8

y - 5 = 8x - 16

y = 8x - 16 + 5

y = 8x - 11

---

johnmulu answered the question on March 7, 2017 at 13:41

Next: a) The nth term of a sequence is given as 3^{(m + 1)} - 2m.
Previous: The sides of triangles were measured and recorded as 8.4 cm, 10.5 cm and 15.3 cm. Calculate the percentage error in perimeter

View More Mathematics Questions and Answers | Return to Questions Index

Exams With Marking Schemes

• Grade 1
• Grade 2
• Grade 3
• Grade 4
• Grade 5
• Grade 6
• Grade 7
• Grade 8
• Grade 9
• PP1
• PP2
• Playgroup
• Form 1
• Form 2
• Form 3
• Form 4

Related Questions

• a) The nth term of a sequence is given as 3^{(m + 1)} - 2m.(Solved)
  

  a) The nth term of a sequence is given as 3^{(m + 1)} - 2m. Find the 5th term of the sequence
  b) Atieno was employed by NGO on contract for a certain number of years. Her basic annual salary for the first year was sh 580 000 and her last basic annual salary was sh 630 400. By end of contract she had earned a total basic salary of sh 4 841 600. If the annual increment was constant, calculate
  i) The period of the contract
  ii) The annual increment
  iii) The annual basic salary in the third year of contract
  

  Date posted: March 7, 2017.  Answers (1)

• Expand (2 + 2x)⁵ in ascending powers of x up to the term x³ (Solved)
  

  a) Expand (2 + 2x)⁵ in ascending powers of x up to the term x³
  b) Hence use your expansion in a) above to evaluate (2.03)⁵ to 3 s.f.
  

  Date posted: March 7, 2017.  Answers (1)

• Solve the equation 4sin (2x + 30)^o = -$\sqrt3$ in the range -90^o < x <180^o(Solved)
  

  Solve the equation
  4sin (2x + 30)^o = -$\sqrt3$ in the range -90^o < x <180^o

  Date posted: March 7, 2017.  Answers (1)

• Find the radius of the circum-circle of a triangle in which angle A = 69^o and a = 3.95 cm.(Solved)
  

  Find the radius of the circum-circle of a triangle in which angle A = 69^o and a = 3.95 cm. Give your answer to four significant figures

  Date posted: March 7, 2017.  Answers (1)

• Evaluate$\frac{2}{2 +\sqrt3} + \frac{2 \sqrt3}{2 - \sqrt3} = a + b\sqrt3$(Solved)
  

  Given that
  $\frac{2}{2 +\sqrt3} + \frac{2 \sqrt3}{2 - \sqrt3} = a + b\sqrt3$
  where a and b are rational numbers. Find the values of a and b

  Date posted: March 7, 2017.  Answers (1)

• Two points P and Q lies on latitude 65^oS. Their longitudes are 96^oE and 84^oW respectively. Find the measured along parallel of latitude. (Take R = 6370 km) (Solved)
  

  Two points P and Q lies on latitude 65^oS. Their longitudes are 96^oE and 85^oW respectively. Find the measured along parallel of latitude. (Take R = 6370 km)
  

  Date posted: March 7, 2017.  Answers (1)

• For a given set of data the variance is (2 + x) and the standard deviation is 1.5. Find the value of x(Solved)
  

  For a given set of data the variance is (2 + x) and the standard deviation is 1.5. Find the value of x

  Date posted: March 7, 2017.  Answers (1)

• A man accumulates sh 71 105 after investing sh 50 000 at a rate of 18% p.a. compounded quarterly. Find the time in years taken to accumulate the amount(Solved)
  

  A man accumulates sh 71 105 after investing sh 50 000 at a rate of 18% p.a. compounded quarterly. Find the time in years taken to accumulate the amount

  Date posted: March 7, 2017.  Answers (1)

• The equation of the line L₁ is 5y + 2x + 8 = 0 and L₂ passes through the points (-5,0) and(5, -4). (Solved)
  

  The equation of the line L₁ is 5y + 2x + 8 = 0 and L₂ passes through the points (-5,0) and(5, -4). Without drawing the lines L₁ and L₂, show that the lines are parallel to each other

  Date posted: March 7, 2017.  Answers (1)

• Make x the subject of the formula -n =$\sqrt{\frac{Mx \; - d}{x \; + y}}$(Solved)
  

  Make x the subject of the formula
  -n =$\sqrt{\frac{Mx \; - d}{x \; + y}}$

  Date posted: March 7, 2017.  Answers (1)

• A bus left Nairobi at 8. 00 a.m and travelled towards Kisumu at an average speed of 80 km/hr.(Solved)
  

  A bus left Nairobi at 8. 00 a.m and travelled towards Kisumu at an average speed of 80 km/hr. At 8.30 a.m a car left Kisumu towards Nairobi at an average speed of 120 km/hr. Given that the distance between Nairobi and Kisumu is 400 km, calculate.
  a) The time the car arrived in Nairobi
  b) The time the two vehicles met
  c) The distance from Nairobi to the meeting point
  

  Date posted: March 7, 2017.  Answers (1)

• Determine the amplitude and the period for the graph of (Solved)
  

  Determine the amplitude and the period for the graph of
  6 sin ($\frac{x}{2} - 90^o$)

  Date posted: March 7, 2017.  Answers (1)

• A man deposits his money in a saving bank on monthly basis. Each deposit exceeds the previous by sh 750. If he deposited sh 1500 initially, (Solved)
  

  A man deposits his money in a saving bank on monthly basis. Each deposit exceeds the previous by sh 750. If he deposited sh 1500 initially, how much money will he have deposited in 12 months

  Date posted: March 7, 2017.  Answers (1)

• The equation of a circle 2x² + 8x + 2y² - 10 = 0. Find the radius and the center of the circle(Solved)
  

  The equation of a circle
  2x² + 8x + 2y² - 10 = 0. Find the radius and the centrer of the circle

  Date posted: March 7, 2017.  Answers (1)

• In the expression (x + 2)^x, the sum of the first two terms is 768. Find the value x(Solved)
  

  In the expression (x + 2)^x, the sum of the first two terms is 768. Find the value x

  Date posted: March 7, 2017.  Answers (1)

• A farmer has 1 200 m wire to fence three sides of a rectangular paddock. The fourth side is a wall. Find the dimensions that will give the maximum possible area.(Solved)
  

  A farmer has 1 200 m wire to fence three sides of a rectangular paddock. The fourth side is a wall. Find the dimensions that will give the maximum possible area.

  Date posted: March 7, 2017.  Answers (1)

• A quantity T is partly constant and partly varies as the square root of S. a) Using k and m as the constants, write down an equation connecting T and S(Solved)
  

  A quantity T is partly constant and partly varies as the square root of S.
  a) Using k and m as the constants, write down an equation connecting T and S
  b) If S = 16 when T = 24 and S = 36 when T = 32, find the value of the constants

  Date posted: March 7, 2017.  Answers (1)

• Solve for x in 2(log₂x)² - 7log₂x + log₂8 = 0(Solved)
  

  Solve for x in
  2(log₂x)² - 7log₂x + log₂8 = 0
  Give your answer in surd form

  Date posted: March 7, 2017.  Answers (1)

• $\frac{\sqrt5 -2\sqrt3}{\sqrt2 + \sqrt{12}}$ is expression in surd form(Solved)
  

  $\frac{\sqrt5 -2\sqrt3}{\sqrt2 + \sqrt{12}}$ is expression in surd form
  i) Write down the conjugate of the denominator in its simplest form
  ii) Hence use the conjugate in (i) above to rationalize the denominator in the expression above

  Date posted: March 7, 2017.  Answers (1)

• The dimensions of a rectangle are given as 8 cm by 5 cm. If A is the area of the rectangle and P is perimeter, determine the maximum possible value of (Solved)
  

  The dimensions of a rectangle are given as 8 cm by 5 cm. If A is the area of the rectangle and P is perimeter, determine the maximum possible value of
  A $\div$ P.

  Date posted: March 7, 2017.  Answers (1)