Application of Derivatives
Find the maximum are of the isosceles triangle inscribed in the ellipse a2x2+b2y2=1,with its vertex at one end of major axis.
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Prove that the function f given by f(x)=x2−x+1is neither strictly increasing nor strictly decreasing on (1,1).
Find the maximum area of an isosceles triangle inscribed in the ellipse a2x2+b2y2=1with its vertex at one end of the major axis.
Show that of all the rectangles inscribed in a given fixed circle, the square has the maximum area.
Find the equation of all lines having slope 2 and being tangent to the curve y+x−32=0.
The line y=x+1is a tangent to the curve y2=4xat the point(A) (1,2) (B)(2,1) (C) (1,2) (D) (1,2)
A window is in the form of a rectangle surmounted by a semicircular opening. The total perimeter of the window is 10 m. Find the dimensions of the window to admit maximum light through the whole opening.
Show that the function f given by f(x)=x3−3x2+4x,x∈Ris strictly increasing on R.
Find the absolute maximum and minimum values of the function f given by f(x)=cos2x+sinx,x∈[0,π]