Application of Derivatives
The volume of a cube is increasing at a rate of 9 cubic centimetres per second. How fast is the surface area increasing when the length of an edge is 10 centimetres?
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Find the value of a
has three distinct real roots.
Find the approximate change in the volume V
of a cube of side x
meters caused by increasing side by 1%˙
If φ(x) is differentiable function ∀x∈R and a∈R+ such that φ(0)=φ(2a),φ(a)=φ(3a)andφ(0)=φ(a) then show that there is at least one root of equation φprime(x+a)=φprime(x)∈(0,2a)
Separate the intervals of monotonocity of the function:
If the tangent at (1,1)
meets the curve again at P,
then find coordinates of P˙
be differentiable function and g(x)
be twice differentiable function. Zeros of f(x),gprime(x)
, respectively, (a<b)˙
Show that there exists at least one root of equation fprime(x)gprime(x)+f(x)gx=0
be the length of one of the equal sides of an isosceles triangle, and let θ
be the angle between them. If x
is increasing at the rate (1/12) m/h, and θ
is increasing at the rate of 180π
radius/h, then find the rate in m3
at which the area of the triangle is increasing when x=12mandthη=π/4.
If it has a maximum at x=−3,
then find the value of a˙