NORTH SOUTH UNIVERSITY
Committed to the highest standards of academic excellence
School of Engineering & Physical Sciences
Department of Mathematics & Physics
Marks: 50
Final Examination
MAT 120.9| Mdt
Course Code: MAT 120, Section: 23
Fall 2020
Time: 50 mins
Answer Q. no 6. and any four (04) of the questions 1-5
1. Find the slope of the tangent line to the curve at the given points by implicit differentiation.
2. Find: (a) the intervals on which is increasing, (b) the intervals on which is decreasing, (c) the open
intervals on which is concave up, (d) the open intervals on which is concave down. The function is f(x)
= 8-12x-x2
3. (a) Use both the first and second derivative tests to show that
has a relative minimum at
.
(b) Find the general form of a function whose second derivative is 6 .
4. Use the given derivative to find all critical points of , and at each critical point determine whether a
relative maximum, relative minimum, or neither occurs. Assume in each case that is continuous
everywhere.
(i)
5. Find an equation of the curve that satisfies the given conditions.
a. At each point
on the curve the slope is 8x+1; the curve passes through the point (-6,0).
b. At each point
on the curve the slope is
; the curve passes through the point (0,8).
6. Evaluate the integral
a.
b.
c.
d.
Prof. Dr. Mohammed Abdul Basith | Mdt