Application of Derivatives
Find the points at which the function f given by f(x)=(x−2)4(x+1)3has(i) local maxima (ii) local minima (iii) point of inflexion
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Find the absolute maximum and minimum values of a function f given by f(x)=2x3−15x2+36x+1on the interval (3.02),[1,5].
Prove that the function f given by f(x)=logcosx is strictly decreasing on (0,2π)and strictly increasing on (2π,π)
Find the equation of the tangent to the curve y=(x−2(x−3)x−7 at the point where it cuts the x-axis.
Find the equation of all lines having slope 2 and being tangent to the curve y+x−32=0.
Prove that the function given by f(x)=x3−3x2+3x−100is increasing in R.
If length of three sides of a trapezium other than base are equal to 10cm, then find the area of the trapezium when it is maximum.
Find the equation of the normals to the curve y=x3+2x+6which are parallel to the line x+14y+4=0.
The normal at the point (1,1) on the curve 2y+x2=3is(A) x+y=0 (B) xy=0 (C) x+y+1=0(D) xy=0