Class 12

Math

Calculus

Application of Derivatives

Find the intervals in which the function f given by $f(x)=x_{2}−4x+6$is (a) strictly increasing (b) strictly decreasing

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The graph $y=2x_{3}−4x+2andy=x_{3}+2x−1$ intersect in exactly 3 distinct points. Then find the slope of the line passing through two of these points.

Displacement $s$ of a particle at time $t$ is expressed as $s=21 t_{3}−6t˙$ Find the acceleration at the time when the velocity vanishes (i.e., velocity tends to zero).

For the curve $y=4x_{3}−2x_{5},$find all the points at which the tangent passes through the origin.

Discuss the maxima and minima of the function $f(x)=x_{32}−x_{34}˙$ Draw the graph of $y=f(x)$ and find the range of $f(x)˙$

The two curves $x_{3}−3xy_{2}+2=0$ and $3x_{2}y−y_{3}−2=0$

Find the equation of the tangent to the curve $(1+x_{2})y=2−x,$ where it crosses the x-axis.

Find the distance of the point on $y=x_{4}+3x_{2}+2x$ which is nearest to the line $y=2x−1$

Let $0<a<b<2π I˙ff(x)=∣tanxtanatanbsinxsinasinbcosxcosacosb∣,then$ find the minimum possible number of roots of $f_{prime}(x)=0$ in $(a,b)˙$