Everything Maths Grade 12
7.5 CHAPTER 7. DIFFERENTIAL CALCULUS Exercise 7 - 3 Find f�(x) if f (x) = x^2 − 5 x + 6 x− 2 Find f�(y) if f (y) = √ y. Find ...
CHAPTER 7. DIFFERENTIAL CALCULUS 7.5 Example 9: Finding the Equation of a Tangent to a Curve QUESTION Find the equation of the t ...
7.5 CHAPTER 7. DIFFERENTIAL CALCULUS 1 2 3 4 − 1 − 2 − 3 − 4 4 3 − 2 − − 1 − (^1234) x y �(1; 1) y = x^2 y = 2x− 1 Curve Sketchi ...
CHAPTER 7. DIFFERENTIAL CALCULUS 7.5 Example 10: Calculation of TurningPoints QUESTION Calculate the turning points of the graph ...
7.5 CHAPTER 7. DIFFERENTIAL CALCULUS Determine the x-intercepts by factorising ax^3 + bx^2 + cx + d = 0 and solving for x. Firs ...
CHAPTER 7. DIFFERENTIAL CALCULUS 7.5 Step 5 : Determine the y-coordinates of the turning points by substituting the x values obt ...
7.5 CHAPTER 7. DIFFERENTIAL CALCULUS Step 2 : Determine the y-intercept We find the y-intercepts by finding the value for g(0). ...
CHAPTER 7. DIFFERENTIAL CALCULUS 7.5 g(x) =−x^3 + 6x^2 − 9 x + 4 g(3) =−(3)^3 + 6(3)^2 − 9(3) + 4 =−27 + 54− 27 + 4 = 4 Therefor ...
7.5 CHAPTER 7. DIFFERENTIAL CALCULUS More practice video solutions or help at http://www.everythingmaths.co.za (1.) 01fy (2.) 01 ...
CHAPTER 7. DIFFERENTIAL CALCULUS 7.6 (3; 1) � x y From this drawing, the point (3; 1) is a horizontal point ofinflexion, because ...
7.6 CHAPTER 7. DIFFERENTIAL CALCULUS We have seen that the coordinates of the turningpoint can be calculatedby differentiating t ...
CHAPTER 7. DIFFERENTIAL CALCULUS 7.6 P�(a) = 10− 2 a 0 = 10− 2 a 2 a = 10 a = 10 2 a = 5 Substitute into (7.26) tosolve for the ...
7.6 CHAPTER 7. DIFFERENTIAL CALCULUS However, we can use (7.25) to write w in terms of l: w = 160 m− 2l (7.26) Substitute (7.26) ...
CHAPTER 7. DIFFERENTIAL CALCULUS 7.6 y 3 x 4 x 5 x (a) Show that y = 1200 cm^2 − 4 x^2 5 x . (b) Find the value of x for which t ...
7.6 CHAPTER 7. DIFFERENTIAL CALCULUS taneous rate of change isthe derivative. When average rate of change is required, it will b ...
CHAPTER 7. DIFFERENTIAL CALCULUS 7.6 Velocity after 1 ,5 s: v(1,5) = 20− 10(1,5) = 5 m· s−^1 Step 3 : Zero velocity v(t) = 0 20 ...
7.6 CHAPTER 7. DIFFERENTIAL CALCULUS f (x) = x^2 − 6 x f (x) = 2x−x^2 Given: f (x) =−x^2 + 3x, find f�(x) using first principle ...
CHAPTER 7. DIFFERENTIAL CALCULUS 7.6 (a) After doing some research, a transport company has determinedthat the rate at which pe ...
Linear Programming 8 8.1 Introduction EMCBP In Grade 11 you wereintroduced to linear programming and solved problems by looking ...
CHAPTER 8. LINEAR PROGRAMMING 8.3 5 10 15 20 5 10 15 20 y = x x = 20 x y Figure 8.1: The feasibleregion corresponding tothe cons ...
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