Application of Derivatives
For the curve y=4x3−2x5,find all the points at which the tangent passes through the origin.
Let x 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 / h at which the area of the triangle is increasing when x=12mandthη=π/4.
There is a point (p,q) on the graph of f(x)=x2 and a point (r,s) on the graph of g(x)=x−8,wherep>0andr>0. If the line through (p,q)and(r,s) is also tangent to both the curves at these points, respectively, then the value of P+r is_________.
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)
The two equal sides of an isosceles triangle with fixed base b are decreasing at the rate of 3cm/s˙ How fast is the area decreasing when the two equal sides are equal to the base?