Find the value(s) of t for which the tangents to is/are horizontal.
B) 0

Question

Find the value(s) of t for which the tangents to  is/are horizontal.
B) 0

Quizplus · Accepted Answer

For a tangent to be horizontal, the slope of the tangent must be 0. The slope of a tangent to a curve at a point is given by the derivative of the curve at that point. Therefore, to find the value(s) of t for which the tangents to the curve in question are horizontal, we need to find the value(s) of t for which the derivative of the curve is equal to 0.

Taking the derivative of the given curve, we get:

dy/dx = -(3/2)t^2 - 8t

Setting this equal to 0 and solving for t, we get:

-(3/2)t^2 - 8t = 0
t(3t + 16) = 0
t = 0 or t = -16/3

Therefore, the only value of t for which the tangents to the curve in question are horizontal is t = 0, which corresponds to choice B.

Find the Value(s) of T for Which the Tangents to