question_answer17) Show that f(x) = 3x + 17 is strictly increasing on R.
View Answer play_arrowquestion_answer18) Show that f(x) = e2x is strictly increasing on R.
View Answer play_arrowquestion_answer24) Find the value of x for which = [x (x – 2)]2 is an increasing function.
View Answer play_arrow question_answer25)
Prove
that 
is an
increasing function of 
in
question_answer26)
Prove
that logarithmic function is strictly increasing on 
question_answer27) Prove that f(x) = x2 – x + 1 is neither increasing nor decreasing on (–1, 1).
View Answer play_arrow question_answer30)
Prove that f(x) = log sin x is strictly increasing on 
and
strictly decreasing on 
question_answer32) Prove that f(x) = [x3 – 3x2 + 3x – 100] is increasing on R.
View Answer play_arrowquestion_answer33) Find the slope of the tangent to curve = 3x4 – 4x at x = 4.
View Answer play_arrow question_answer34)
Find
the slope of the tangent to curve
question_answer36) Find the slope of tangent to curve = x3 – 3x + 2 at x = 3.
View Answer play_arrow question_answer37)
Find
the slope of the normal to the curve
question_answer38)
Find the slope of normal to the curve x = 1 ? a sin 
question_answer41) Find the point on the curve y = x3 – 11x + 5 at which the tangent is y = x – 11.
View Answer play_arrow question_answer42)
Find the equation of all lines having slope ?1 that are
tangents to the curve 
question_answer43)
Find the equation of all lines
having slope 2 which are tangent to the curve
question_answer44)
Find equation of all lines having
slope 0 which are tangent to the curve 
question_answer52) Find the equation of normal at (am2, am3) for the curve ay2 = x3.
View Answer play_arrowquestion_answer56) Prove that the curve x = y2 and xy = K cut at right angles if 8K2 = 1.
View Answer play_arrow question_answer57)
Find the equation of the tangent and normal to the
hyperbola 
at (x0,
y0).
question_answer59) Find the approximate value of f(2.01) where f(x) = 4x2 + 5x + 2.
View Answer play_arrowquestion_answer60) Find the approximate value of f(5.001) where f(x) = x3 – 7x2 + 15.
View Answer play_arrow question_answer71)
At what in the
interval [0, 
, does the
function sin 2x attain its maximum value ?
question_answer72) What is the maximum value of the function sin x + cos x?
View Answer play_arrow question_answer75)
Find the maximum and
minimum values of x + sin 2x on [0, 
]
question_answer76) Find two numbers whose sum is 24 and whose product is as large as possible.
View Answer play_arrowquestion_answer77) Find two positive number x and y such that x + y = 60 and xy3 is maximum.
View Answer play_arrowquestion_answer79) Find two positive numbers whose sum is 16 and sum of whose cubes is minimum.
View Answer play_arrow question_answer91)
Show that the function
given by f(x) 
has
maximum at x = e.
question_answer93) Find the equation of the normal to the curve y2 = 4x at (1, 2).
View Answer play_arrow question_answer102)
Find the absolute maxima and minimum values of f(x) = cos2x
+ sin x, 
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