Question

HELP PLEASE

Answer 1

I need help with #4.

Answer 2

Here is the problem.

Answer 3

@mathmale @518nad @IrishBoy123 @Directrix

Answer 4

Sorry to say, your derivates need work. t*e^t is a product, and thus you must use the product rule to differentiate it. Please give this a try.
Your handwritten work is exceptionally neat and deserves praise.

Answer 5

double check y'

Answer 6

Of course..... Thanks!

Answer 7

My pleasure. Triciaal noticed the same problem.

Answer 8

derivatives (not derivates). Mea culpa. ;(

Answer 9

Haha xD

Answer 10

How would I find its concavity?

Answer 11

Find the 2nd derivative
Set it = to 0
Solve for all t values
Plot the t values on a number line
Identify intervals on which the 2nd deriv. is + and those on which the 2nd deriv. is -

Answer 12

is there another way to say that?

Answer 13

On any interval on which the 2nd deriv. is +, your graph is concave upward; if -, downward.

Answer 14

If y'=0 produces a root or two, you may have an inflection point at any such value.