Engineering Mathematics
Calculus
Differential Calculus
Questions mapped to Differential Calculus under Calculus.
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IncorrectLet be a real-valued function whose second derivative is positive for . Which of the following statements is/are always true?
has at least one local minimum.
cannot have two distinct local minima.
has at least one local maximum.
The minimum value of cannot be negative.
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Sign in to UnlockConsider the function for , where denotes the maximum of and . Which of the following statements is/are true?
is not differentiable.
is differentiable and its derivative is continuous.
is differentiable but its derivative is not continuous.
and its derivative are differentiable.
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Sign in to UnlockConsider the following equation in a 2-D real-space.
Which of the following statement(s) is/are true.
When , the area enclosed by the curve is .
When tends to , the area enclosed by the curve tends to 4.
When tends to 0, the area enclosed by the curve is 1.
When , the area enclosed by the curve is 2.
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Sign in to UnlockA quadratic function of two variables is given as
The magnitude of the maximum rate of change of the function at the point is ________ (Round off to the nearest integer).
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Sign in to UnlockLet . Then decreases in the interval.
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Sign in to UnlockLet . The direction in which the function increases most rapidly at point is
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Sign in to UnlockLet be a real-valued function such that for some and for all . Then has
two distinct local minima in
exactly one local minimum in
one local maximum in
no local minimum in
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Sign in to UnlockSuppose the circles and intersect each other orthogonally at the point (u,v). Then __________.
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Sign in to UnlockIn the open interval , the polynomial has
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Sign in to Unlockis a polynomial on real over real coefficients wherein. Which of the following statements is true?
No choice of coefficients can make all roots identical.
a, b, c, d can be chosen to ensure that all roots are complex.
d can be chosen to ensure that is a root for any given set .
c alone cannot ensure that all roots are real.
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Sign in to UnlockFor real numbers, and with , the maximum and minimum value of for are respectively _________.
7 and
7 and 1
-2 and
1 and
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Sign in to UnlockLet f be a real-valued function of a real variable defined as, where denotes the largest integer less than or equal to x. The value ofis _______ (up 0.25 to 2 decimal places).
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Sign in to UnlockLet f be a real-valued function of a real variable defined as for, andfor x < 0. Which one of the following statements is true?
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Sign in to UnlockLet. The maximum value of f(x) over the interval [0, 2] is _____ (up to 1 decimal place).
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Sign in to UnlockA function f(x) is defined as . Which one of the following statements is TRUE?
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Sign in to UnlockConsider a function f(x,y,z) given by . The partial derivative of this function with respect to x at the point, x = 2, y = 1 and z = 3 is __________ .
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Sign in to UnlockLet
Consider the composition of f and g. i.e., 
. The number of discontinuities in 
present in the interval is:
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Sign in to UnlockThe maximum value attained by the function in the interval [1, 2] is ______________.
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Sign in to UnlockIf a continuous function f(x) does not have a root in the interval [a, b], then which one of the following statement is TRUE?
f(a) . f(b) = 0
f(a) . f(b) < 0
f(a) . f(b) > 0
f(a)/f(b)
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Sign in to UnlockGiven , where f, g, h are complex valued functions of a complex variable z. Which one of the following statements is TRUE?
If f(z) is differentiable at , then g(z) and h(z) are also differentiable at .
If g(z) and h(z) are differentiable at , then f(z) is also differentiable at .
If f(z) is continuous at , then it is differentiable at .
If f(z) is differentiable at , then so are its real and imaginary parts.
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Sign in to UnlockLet . The maximum value of the function in the interval is
e
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Sign in to UnlockMinimum of the real valued function occurs at x equal to
0
1
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Sign in to UnlockThe minimum value of the function in the interval [-3, 3] is
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Sign in to UnlockA function is defined over an open interval x= (1, 2). At least at one point in this interval, is exactly
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Sign in to UnlockThe maximum value of in the interval [1, 6] is
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Sign in to UnlockRoots of the algebraic equation are
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Sign in to UnlockThe function has
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Sign in to UnlockAt t = 0, the function has
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Sign in to UnlockA cubic polynomial with real coefficients
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Sign in to UnlockConsider function where x is a real number. Then the function has
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Sign in to UnlockFor the function, the maximum occurs when x is equal to:
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