Class 12

Math

Calculus

Application of Derivatives

The line $y=x+1$is a tangent to the curve $y_{2}=4x$at the point(A) $(1,2)$ (B)$(2,1)$ (C) $(1,2)$ (D) $(1,2)$

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Draw the graph of $f(x)=x_{2}−xx_{2}−5x+6 $

Find the shortest distance between the line $y=x−2$ and the parabola $y=x_{2}+3x+2.$

Find the point on the curve where tangents to the curve $y_{2}−2x_{3}−4y+8=0$ pass through (1,2).

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 $f(x)˙$

Let $y=f(x)$ be drawn with $f(0)=2$ and for each real number $a$ the line tangent to $y=f(x)$ at $(a,f(a))$ has x-intercept $(a−2)$. If $f(x)$ is of the form of $ke_{px}$ then$pk $ has the value equal to

Let $f(x)$ be defined as $f(x)={tan_{−1}α−5x_{2},0<x<1and−6x,x≥1$ if $f(x)$ has a maximum at $x=1,$ then find the values of $α$ .

Find the maximum and minimum values of the function $y=(g)_{e}(3x_{4}−2x_{3}−6x_{2}+6x+1)∀x∈(0,2)$ Given that$(3x_{4}−2x_{3}−6x_{2}+6x_{2}+6x+1)>0Ax∈(0,2)$

Find the angle at which the curve $y=Ke_{Kx}$ intersects the y-axis.