The values of p for which the function
f(x)=x^{5} – 3x + ln 5 decreases for all real x is
For which values of `a' will the function
f(x) = x^{4} + ax^{3} + + 1 will be concave upward along the entire real line
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The function f(x) = x(x + 3) e^{–x/2} satisfies all the conditions of Rolle's theorem in [–3, 0]. The value of c which verifies Rolle's theorem, is
For what values of a does the curve
f(x) = x(a^{2} – 2a – 2) + cos x is always strictly monotonic x ∈ R.
If the function f(x) = x^{3} – 6ax^{2} + 5x satisfies the conditions of Lagrange's mean theorem for the interval [1, 2] and the tangent to the curve y = f(x) at x = 7/4 is parallel to the chord joining the points of intersection of the curve with the ordinates x = 1 and x = 2. Then the value of a is
The function f(x) = tan^{1} (sin x + cos x) is an increasing function in
A function y = f(x) has a second order derivative f" = 6(x – 1). If its graph passes through the point (2, 1) and at that point the tangent of the graph is y = 3x – 5, then the function is
If f(x) = [a sin x + b cosx] / [c sin x + d cos x] is monotonically increasing, then
If f(x) = 1 + x ln and g(x) = then for x ³ 0
The set of values of the parameter `a' for which the function; f(x) = 8ax – a sin 6x – 7x – sin 5x increases & has no critical points for all x Î R, is
f : [0, 4] → R is a differentiable function then for some a, b Î (0, 4), f^{2}(4) – f^{2}(0) equals
Let f(x) = ax^{4} + bx^{3} + x^{2} + x – 1. If 9b^{2} < 24a, then number of real roots of f(x) = 0 are
If f(x) = (x – 1) (x – 2) (x – 3) (x – 4), then roots of f'(x) = 0 not lying in the interval
If f(x) = 1 + x^{m} (x – 1)^{n}, m, n ∈ N, then f'(x) = 0 has atleast one root in the interval
204 videos288 docs139 tests

Maxima and Minima of a Function Video  13:57 min 
JEE Advanced Level Test: Maxima and Minima Test  30 ques 
Finding maxima and minima Using First Derivative Test (with Example) Video  09:27 min 
Examples: Rate of change of quantities Video  11:50 min 
JEE Advanced Level Test: Maxima and Minima 2 Test  19 ques 
204 videos288 docs139 tests

Maxima and Minima of a Function Video  13:57 min 
JEE Advanced Level Test: Maxima and Minima Test  30 ques 
Finding maxima and minima Using First Derivative Test (with Example) Video  09:27 min 
Examples: Rate of change of quantities Video  11:50 min 
JEE Advanced Level Test: Maxima and Minima 2 Test  19 ques 