Application of Derivatives
Find the approximate value of f(5.001), where f(x)=x3−7x2+15.
Prove that if 2a02<15a, all roots of x5−a0x4+3ax3+bx2+cx+d=0 cannot be real. It is given that a0,a,b,c,d∈R˙
Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is 32R
If 2a+3b+6c=0, then prove that at least one root of the equation ax2+bx+c=0 lies in the interval (0,1).
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.
On the curve x3=12y, find the interval of values of x for which the abscissa changes at a faster rate than the ordinate?