Application of Derivatives
Prove that the following functions do not have maxima or minima:(i) f (x) = ex (ii) g(x)=logx(iii) h(x)=x3+x2+x+1
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Points on the curve f(x)=1−x2x
where the tangent is inclined at an angle of 4π
to the x-axis are
(0,0) (b) (3,−23)
For the curve y=f(x) prove that (lenght n or mal)^2/(lenght or tanght)^2
The acute angle between the curves y=∣∣x2−1∣∣and y=∣∣x2−3∣∣ at their points of intersection when when x> 0, is
Find the shortest distance between the line y=x−2
and the parabola y=x2+3x+2.
Prove that all the point on the curve y=x+sinx
at which the tangent is parallel to x-axis lie on parabola.
The curve f(x)=x−10x2+ax+6
has a stationary point at (4,1)
. Find the values of aandb
. Also, show that f(x)
has point of maxima at this point.
Discuss the extrema of f(x)=1+xtanxx,x∈(0,2π)
Find the condition if the equation 3x2+4ax+b=0
has at least one root in (0,1)˙