Calculus Math Exam Quiz!

9 Questions | Total Attempts: 46

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Calculus Math Exam Quiz!

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Questions and Answers
  • 1. 
    Determine: lim(x->4)[(x2-16)/(x-4)]  [Blank]
  • 2. 
    Use first principles to determine the derivative of f if:
    1. f(x)=x2+5 [Blank]
    2. f(x)=-2x2  [Blank]
    3. f(x)=x2/5 [Blank]
  • 3. 
    Use the rules of derivatives to determine the derivative of g if:
    1. g(x)=x2+3x+5 [Blank]
    2. g(x)=5x2-x-3  [Blank]
  • 4. 
    The graphs of the parabola f(x)=3x2+2, and the straight lines g and h are represented in the sketch. g is a tangent to f at the point A and h is perpendicular to g at A. The coordinates of A are (1;5).
    1. Determine the equation of the tangent g
    2. Determine the equation of h
    round off at the final answer to 2 decimal places and use a full stop (.) as your decimal point g=[Blank] h=[Blank]
  • 5. 
    A function is defined by the equation y=x3+ax2+bx+c Q(0;4) is a turning point on the graph of y. And a local minimum occurs at a point R where y=0. P is a point on the graph with the coordinates (-1,0)
    1. Calculate the values of a, b and c.
    a= [Blank] b=[Blank] c=[Blank] and Determine the coordinates of R R=[Blank]
  • 6. 
    A function f is defined by y=px3+5x2-qx-3.The graph has a turning point at (-2;9). Calculate the values of p and q
    1. p= [Blank]
    2. q=[Blank]
  • 7. 
    The sketch alongside shows the curve of f(x)=x3-x2-8x+12 The curve has a y-intercept at (0;12) and turning points at (2;0) and B. The point A is an x-intercept SEPARATE COORDINATES WITH ;
    1. Calculate the Coordinates of A
    2. Calculate the x-coordinate of B
    3. Calculate the coordinates of the point of inflection
    A= [Blank] x coordinate of B=[Blank] POF=[Blank]  
  • 8. 
    A factory has x employees and makes a profit of P rand per week. The relation between the profit and the number of employees is expressed by the formula P=-2x3+600x+1000 Calculate:
    1. The number of employees, x, for the factory to make a maximum profit
    2. The maximum profit
    x=[Blank] P=[Blank]
  • 9. 
    The height to which a plant grows during the first six months is given by the following function: f(x)=36x-3x2 ; 0<=x<=6 where x is the age of the plant in months and f(x) the height in centimeters above the ground after x months.
    1. What height would the plant reach after 3 months? [Blank]
    2. At the end of how many months will the plant reach its maximum height [Blank]
    3. Hence calculate the maximum height to which the plant will grow [Blank]