Application of Derivatives
Find the maximum and the minimum values, if any, of the function f given byf(x)=x2,x∈R.
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Find the equations of the normal to the curve y=x3+2x+6
which are parallel to the line x+14y+4=0.
Using Lagranges mean value theorem, prove that ∣cosa−cosb∣≤∣a−b∣˙
Points on the curve f(x)=1−x2x
where the tangent is inclined at an angle of 4π
to the x-axis are
(0,0) (b) (3,−23)
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.
Discuss the extremum of f(x)=31(x+x1)
Find the range of the function
Discuss the extremum of f(x)=2x+3x32
The latest edge of a regular hexagonal pyramid is 1cm˙
If the volume is maximum, then find its height.