a) f(x)= c) f(x)= e) f(x)= sin x COS X In x Differentiate then simply each...

 

 

Transcribed Image Text:

a) f(x)= c) f(x)= e) f(x)= sin x COS X In x Differentiate then simply each of the following: b) f(x)= d) (x)= x + 1 sin x In x sin x f) f(x)=- 10. [A/5 MARKS] Find the intervals of concavity for the following functions: a) f(x) = xex b) f(x) = x ln x 7. [T/6 MARKS] For what value of the constant c is the following function continuous at every number? (x+c if x <2 f(x)=x +1_if x2 8. [T/6 MARKS] If 2700 cm of material is available to make a box with a square base and open top, find the dimensions of the box that give the largest volume of the box. What is the maximum value of the volume? 5. [C/ 4 MARKS] Consider the function f(x) defined by the following graph: 4 VA 3 -1 For each value of x = a, classify the function f(x) as continuous, having a jump, a removable or an infinite discontinuity. a) a= -3 b) a = -1 b) f(x) = 2x-1 2x+1 3 c) a= 2 6. [K/4 MARKS] For each case, find the average rate of change over each interval. a) f(x) = x4 x + x [-1, 1] [0, 2] d) a = 0 a) f(x)= c) f(x)= e) f(x)= sin x COS X In x Differentiate then simply each of the following: b) f(x)= d) (x)= x + 1 sin x In x sin x f) f(x)=- 10. [A/5 MARKS] Find the intervals of concavity for the following functions: a) f(x) = xex b) f(x) = x ln x 7. [T/6 MARKS] For what value of the constant c is the following function continuous at every number? (x+c if x <2 f(x)=x +1_if x2 8. [T/6 MARKS] If 2700 cm of material is available to make a box with a square base and open top, find the dimensions of the box that give the largest volume of the box. What is the maximum value of the volume? 5. [C/ 4 MARKS] Consider the function f(x) defined by the following graph: 4 VA 3 -1 For each value of x = a, classify the function f(x) as continuous, having a jump, a removable or an infinite discontinuity. a) a= -3 b) a = -1 b) f(x) = 2x-1 2x+1 3 c) a= 2 6. [K/4 MARKS] For each case, find the average rate of change over each interval. a) f(x) = x4 x + x [-1, 1] [0, 2] d) a = 0