`g(t)={(max(t^3-6t^2+9t-3,0), , t in[0,3]),(4-t,,tin(3,4)):}` , find the point of non-differentiability

Let a function g : [0,4] to R be defined as g(t)={(max(t^3-6t^2+9t-3,0), , t in[0,3]),(4-t,,tin(3,4)):} then the number of points in the interval (0,4) where g(x) is NOT differentiable, is _____________.

t^(3)+t^(2)+t+6=0

Given that x=120-15t-6t^(2)+t^(3)(tgt0) , find the time when the velocity is zero. Find the displacement at this instant.

If S=(t^(3))/(3)-2t^(2)+3t+4 , then

If B-A^(T)={:[(3,4,-2),(5,-3,7)]:}andB^(T)+A={:[(2,0),(5,-1),(3,4)]:} , then find Matrix A.

f(x)=x^(2)-2|x|,g(x)=min f(t):0<=t<=x,-2<=x<=0 and max f(t):0<=t<=x,0<=x<=3 Sketch the graph of g(x) and discuss its differentiability

The vertices of a triangle are [a t_1t_2,a(t_1 +t_2)], [a t_2t_3,a(t_2 +t_3)], [a t_3t_1,a(t_3 +t_1)] Then the orthocenter of the triangle is (a) (-a, a(t_1+t_2+t_3)-at_1t_2t_3) (b) (-a, a(t_1+t_2+t_3)+at_1t_2t_3) (c) (a, a(t_1+t_2+t_3)+at_1t_2t_3) (d) (a, a(t_1+t_2+t_3)-at_1t_2t_3)

Statement-I If a circle S=0 intersect hyperbola xy=4 at four points, three of them being (2, 2), (4, 1) and (6, (2)/(3) , then the coordinate of the fourth point are ((1)(4), 16) . Statement-II If a circle S=0 intersects a hyperbola xy=c^(2) at t_1, t_2, t_3 and t_4 , then t_1t_2t_3t_4=1

The position of a particle is given by the equation f(t)=t^(3)-6t^(2)+9t where t is measured in second and s in meter. Find the acceleration at time t. What is the acceleration at 4 s?

If f(t)=4t^(2)-3t+6 , find (i) f (0) , (ii) f (4) , (iii) f(-5) .