Question

Determine the concavity of 3sinx +2(cos(2x)^2
at the point x=pi

Answer 1

concavity is determined through the second derivative. Derive that twice and plug in pi for x. If the value is positive, then it is concave up. If negative, then concave down.

Answer 2

i am stuck need help doing the second deeriv

Answer 3

derivative of 3sinx is 3cosx
derivative of 3cosx is -3sinx

Then derivative of that second half requires a chain rule within a chain rule.

similarly, you can also graph that and then graphically determine whether its concavity is positive or negative. (positive if its like cupping upwards and negative if its like an upside down cup)

Answer 4

thanks can you show me the result with chain rule as this is a non calculator section

Answer 5

3cosx-8sin(2x)cos(2x) is the first derivative. Try and piece together how I got that from the chain rule. From there, you use product rule + chain rule to get the 2nd derivative. YOU CAN DO THIS :D

Answer 6

wait

Answer 7

3sinx-8sin2x(-2sin2x)+cos(2x)-8cos2x

Answer 8

how can i do these things with test time limit god help me wednesday,,