Find dy/dx and d2y/dx2, and find the slope and concavity (if possible) at the given value of the parameter. (If an answer does not exist, enter DNE.)

Question

y = 7t − 2 x=t^1/2



Answer 1

x = √t

x² = t for x ≥ 0

y = 7t - 2 = 7x² - 2 for x ≥ 0

dy/dx = 14x

d²y / dx² = 14

No value for parameter t is specified, but slope of tangent line = 14x = 14√t for t ≥ 0

and y is concave up over the same domain since y^" = 14 > 0 for all t ≥ 0.