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Exam (elaborations) CALCULUS (1) PROBLEM SET
Differentiate the function (1) − (4). 
(1) f(x) = (x − 2)(2x + 3). 
(2) y = √ 
x(x − 1). 
(3) y = 
x 
2 − 2√ 
x 
x 
. 
(4) u = √5 t + 4√ 
t5 
. Find an equation of the tangent line to the curve at the given point (5) − (6). 
(5) y = x 
4 + 2e 
x 
, (0, 2). 
(6) y = (1 + 2x) 
2 
, (1, 9). 
(7) Find the points on the curve y = 2x 
3 + 3x + 1, where the tangent is hori- 2 − 12x 
zontal. 
(8) Let f(x) = ( 
2 − x if x ≤
- Exam (elaborations)
- • 11 pages •
Differentiate the function (1) − (4). 
(1) f(x) = (x − 2)(2x + 3). 
(2) y = √ 
x(x − 1). 
(3) y = 
x 
2 − 2√ 
x 
x 
. 
(4) u = √5 t + 4√ 
t5 
. Find an equation of the tangent line to the curve at the given point (5) − (6). 
(5) y = x 
4 + 2e 
x 
, (0, 2). 
(6) y = (1 + 2x) 
2 
, (1, 9). 
(7) Find the points on the curve y = 2x 
3 + 3x + 1, where the tangent is hori- 2 − 12x 
zontal. 
(8) Let f(x) = ( 
2 − x if x ≤