An object moves along a horizontal line according to S=t^2-6t^2+9t. When is S decreasing and increasing?

Question

Please apply application of drivatives.

Answer 1

S = t² - 6t² + 9t

S = -5t² + 9t

 

This is a parabola, not a horizontal line.

The t coordinate of the vertex is at

t = -b/2a = -9/[2(-5)] = 9/10

 

To the left of the vertex the function is increasing

(-∞, 9/10)

To the right of the vertex the function is decreasing 

(9/10,∞)