a particle's motion is described by the equation d=t^2-8t+15 where d and t are measured in meters and seconds. show that the particle is at rest when t=4.
And it was not clear whether the OP could use "rules" of differentiation like that. Since this was posted in "Precalculus" it is likely that he knows only the "limit of the difference quotient" definition of derivative- or that he could find where the slope of the tangent line is 0 by completing the square as Captain Black suggested.we need to integrate velocity which comes out to be 2t-8
The value of corresponding to the vertex is the mid point between the roots of the quadratic obtained by setting displacement to zero:
Applying the quadratic formula to this quadratic give the roots as