The value of Lagrange's mean value theorem for $f(x)=e^x+24$ in $[0,1]$ is

Equation of the normal to the curve $y=x^2+x$ at the point $(1,2)$ is

Displacement $s$ of a particle at time $t$ is expressed as $s=2 t^3-9 t$. Find the acceleration at the time when $b^{t 5}$ velocity vanishes.

If a running track of 500 ft is to be laid out enclosing a playground the shape of which is a rectangle with a semi-circle at each end, then the length of the rectangular portion such that the area of the rectangular portion is to be maximum is (in feet)