Geometrical Meaning of Derivative

Find an equation for the line tangent to the graph of $f\left(x\right)=3x^4-6x+3$ at $x=2.$

 Check the differentiability of $f\left(x\right)=x^{\frac{1}{3}}$ at $x=0.$

A circle of equation $x^2+y^2+ax+by+c=0$ passes through $(0,6)$ and touches $y=x^2$ at $(2,4)$. Find $a+c$?

$P\left(A_1\right)=3/8;P\left(A_2\right)=2/3;P\left(A_1\cap A_2\right)=1/4$ then $A_1$ and $A_2$ will be:

When $\mathrm{r}=1$, all the points in a scatter diagram would lie:

If every observation is increased by 5 then:

${\int }_1^e\frac{e^x\left(x{\log }_{e}x+1\right)}{x}dx$:

If the Harmonic means of two numbers is 4 and Arithmetic mean $\left(\mathrm{A}\right)$ and Geometric mean $\left(\mathrm{G}\right)$ satisfy the equation $2A+G^2=27$ then the two numbers are:

The relation between the parameter ‘$t$’ and the angle $\alpha$ between the tangent to the given curve and the $x$-axis is given by, ‘$t$’ is equal to:

The tangent at any point P of a curve c meets the x axis at Q whose abscissa is positive and OP=OQ, O being the origin. Curve c passes through the point (1, 0) and tangent on point (1, 0) is given by x=a. Then a equals to...........