Application of Derivatives
Prove that the function given by f(x)=x3−3x2+3x−100is increasing in R.
Find the equation of the tangent line to the curve y=x2−2x+7 which is.
(a) parallel to the line 2x−y+9=0.
(b) perpendicular to the line 5y−15x=13.
Find the points of local maxima or local minima and the corresponding local maximum and minimum values of each of the following functions:
Find the rate of change of the area of a circle with respect to its radius r when
(i) r=3 cm
(ii) r=4 cm