The instantaneous rate of change at t = 1 for the function f (t) = te^{−t} + 9 is
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The equation of the tangent to the curve y = e^{2x} at the point (0, 1) is
The smallest value of the polynomial x^{3}−18x^{2}+96 in the interval [0, 9] is
If the graph of a differentiable function y = f (x) meets the lines y = – 1 and y = 1, then the graph
The equation of the tangent to the curve y=(4−x^{2})^{2/3} at x = 2 is
Given that f (x) = x^{1/x} , x>0, has the maximum value at x = e,then
Let f be a real valued function defined on (0, 1) ∪ (2, 4) such that f ‘ (x) = 0 for every x, then
The slope of the tangent to the curve x = a sin t, y = a at the point ‘t’ is
In case of strict decreasing functions, slope of tangent and hence derivative is
Let f (x) = x^{3}−6x^{2}+9x+18, then f (x) is strict decreasing in
Tangents to the curve y = x^{3} at the points (1, 1) and (– 1, – 1) are
Let f(x) = x^{25}(1−x)^{75} for all x ∈ [0,1], then f (x) assumes its maximum value at
The stone projected vertically upwards moves under the action of gravity alone and its motion is described by x = 49 t – 4.9 t^{2} . It is at a maximum height when
Let g (x) be continuous in a neighbourhood of ‘a’ and g (a) ≠ 0. Let f be a function such that f ‘ (x) = g(x) (x−a)^{2} , then
Minimum value of the function f(x) = x^{2}+x+1 is
If the line y=x is a tangent to the parabola y=ax2+bx+c at the point (1,1) and the curve passes through (−1,0), then
At which point the line x/a + y/b = 1, touches the curve y = bex/a
209 videos443 docs143 tests

209 videos443 docs143 tests
