Solving an intial value problem using relative extrema

[DODGEVIPER13]

Homework Statement

See uploaded file. PROBLEM 5

Homework Equations

See uploaded file

The Attempt at a Solution

I am confused on how to go about doing the rest of this I realize I can do it with the first and second derivatives but I forgot what exactly I do with that. I know the first derivative gives me a tangent line to the curve or should I use limits to do this? SEE PROBLEM 5

 

[ehild]

I do not understand what you tried to do. The problem asks the numerical value of y at t=0.8.
What is the value of the first derivative at a local maximum or minimum? Substitute it for y' in the equation.

ehild

 

[DODGEVIPER13]

ok so should I scap my work or just plug .8 into the first derivative of what I did?

 

[ehild]

Answer my question, please. What is the numerical value of the first derivative of any function at a local extreme?

ehild

 

[DODGEVIPER13]

Ok man you got me I really am trying so at a local extreme there has to be a critical point so the value of the derivative at that point equals zero correct?

 

[DODGEVIPER13]

ok so by setting y'=0 and solving for y I get -1.34909.

 

[ehild]

Correct.
You can solve the differential equation, too (although it is not asked) and use this value of y at t=0.8 to get the integration constant. And then the full y(t) function is known.

ehild