“Easy” questions:
Question 1:
Find the slope of the tangent to the curve represented by the curve and
at the point
.
Question 2:
Find the co-ordinates of the point P on the curve , the tangent at which is perpendicular to the line
.
Question 3:
Find the co-ordinates of the point lying in the first quadrant on the ellipse
so that the area of the triangle formed by the tangent at P and the co-ordinate axes is the smallest.
Question 4:
The function , where
is
(a) increasing on
(b) decreasing on
(c) increasing on and decreasing on
(d) decreasing on and increasing on
.
Fill in the correct multiple choice. Only one of the choices is correct.
Question 5:
Find the length of a longest interval in which the function is increasing.
Question 6:
Let , then
is
(a) increasing on
(b) decreasing on
(c) increasing on
(d) decreasing on .
Fill in the correct choice above. Only one choice holds true.
Question 7:
Consider the following statements S and R:
S: Both and
are decreasing functions in the interval
.
R: If a differentiable function decreases in the interval , then its derivative also decreases in
.
Which of the following is true?
(i) Both S and R are wrong.
(ii) Both S and R are correct, but R is not the correct explanation for S.
(iii) S is correct and R is the correct explanation for S.
(iv) S is correct and R is wrong.
Indicate the correct choice. Only one choice is correct.
Question 8:
For which of the following functions on , the Lagrange’s Mean Value theorem is not applicable:
(i) , when
; and
, when
.
(ii) , when
; and
, when
.
(iii)
(iv) .
Only one choice is correct. Which one?
Question 9:
How many real roots does the equation have?
Question 10:
What is the difference between the greatest and least values of the function ?
More later,
Nalin Pithwa.