Mathematics and Mathematical Literacy - Thutong

Mathematics(NSC)/Grade 12/ P1 31 ExemplarQUESTION 54.2.6 There are two x values where the two functions are increasing at thesame rate. Find these values correct to two decimal places. (6)[32]5.1 The following seems to show that 2 = 1. Explain where and why the erroroccurred.line1line 2line 3line 4line 5line 6line 7line 8a2aa( a − b)(a + b)( a + b)b + b2b22− b2========babab − b2b(a − b)bbb1multiply by asubtract bfactorisedivide by a - ba = b so substitute b for a2divide by b(3)5.23 2Given f ( x)= 2x+ x − 7x− 65.2.1 Determine all values of x such that f(x) = 0. (5)5.2.232Hence of otherwise solve: 2( x − 2) + ( x − 2) − 7( x − 2) = 6(3)[11]QUESTION 66.1Determine the derivative of1f ( x)= using first principlesx − 2(5)6.2dyDetermine if dxy =x3+ 2xx − 3(5)6.32For a given function f(x) the derivative is f ′(x)= −x− x + 26.3.1 What is the gradient of the tangent to the function f(x) at x = 0? (1)6.3.2 Where is f(x) increasing? (4)Copyright reserved