$P(5,2)$ is a point on the curve $y=f(x)$ and $\frac{7}{2}$ is the slope of the tangent to the curve at $P$. The area of the triangle (in sq. units) formed by the tangent and the normal to the curve at $P$ with $X$-axis is

If a particle is moving in a straight line so that after $t$ seconds its distance $S$ (in cms) from a fixed point on the line is given by $S=f(t)=t^3-5 t^2+8 t$, then the acceleration of the particle at $t=5 \mathrm{sec}$ is (in $\mathrm{cm} / \mathrm{sec}^2$ )

If $f:[a, b] \rightarrow[c, d]$ is a continuous and strictly increasing function, then $\frac{d-c}{b-a}$ is

The acute angle between the curves $y=3 x^2-2 x-1$ and $y=x^3-1$ at their point of intersection which lies in the first quadrant is