M129: Applied Calculus Tutor Marked Assignment Cut-Off Date:--------, 2015 Total Marks: 40 Contents Feedback form …………………..…………………….…...….. 2 Question 1 …………………………………………………..……… 3 Question 2 …………………..………………..……………………… 3 Question 3 ……………………..……………

M129: Applied Calculus
Tutor Marked Assignment

Cut-Off Date:--------, 2015 Total Marks: 40

Contents
Feedback form …………………..…………………….…...….. 2
Question 1 …………………………………………………..……… 3
Question 2 …………………..………………..……………………… 3
Question 3 ……………………..………………..…………………… 4
Question 4 ………………..………………………..……………… 4
Question 5 …………………………………………………..……… 5
Question 6 …………………………………..……………………… 5
Question 7 …………………………………..…………………… 6
Question 8 ……………………………………..…………………… 6

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M129 TMA Feedback Form


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QUESTION 1 2 3 4 5 6 7 8
MARK 5 5 5 5 5 5 5 5
SCORE
TOTAL




Tutor’s Comments:


This TMA covers only chapters 0, 1, 2, 3 and 4. The TMA consists of eight questions for a total of 40 marks. Please solve each question in the space provided. You should give the details of your solutions and not just the final results.

Q−1: [3+2Marks] Let f(x)= x^2-12x+27 , g(x)= 4x^4-4

Find the zeros of g(x) and f(x).
Find the points of intersection, if any, of the pair of curves :
y=x+3 , x+y=9


Q−2: [2+2+1Marks]
Letf(x)= √(4-x) ,g(x)= x^2+2 .
Find f(g(x)).
Find g(f (x)).
Find the domains of the function f(x)= (5x+4)/(x^2-64 )



Q¬−3: [2+3 Marks]
Use the definition of the derivative to find f ′(x) if
f(x)=9x^2+4x
f(x)= 2/(x+1)




Q−4: [2 + 3 Marks]

Find an equation of the tangent line to the graph of f(x)=〖 (3x+1)〗^2
at the point whose x-coordinate is 3.

Find the slope of the tangent line to the curve x+y =xy, at the point (2, 2).


Q−5:[2.5+2.5 Marks] differentiate the following function:

f(x)=(2x^2+1) ∜( x^2+3)
f(x)= 〖(x+2)〗^3/√(x^2-3)



Q¬−6: [5×1Marks] Let f(x)=2x^4-56x^3+13
Find f ′(x) and f ′′(x).
Find the intervals on which f (x) is increasing or decreasing.
Find the local maximum and minimum of f (x), if any.
Find the intervals on which the graph of f (x) is concave up or concave down.
Find the inflection points of f (x), if any.






Q−7:[5 Marks] find the area of the largest rectangle that can be inscribed in a circle of radius 4




Q¬−8:[5 Marks]Use the logarithmic differentiation to differentiate the function

y= ((x+1)^2 (2x-2))/((x^2-2)〖(2x+3)〗^3 )