critical numbers, upcomming quiz, please help!

[Joey29]

How do you solve for the critical pts. of these two functions?

.25t^4 - 8t

^---- find the derivitive and set it to zero, but because Its to the 4th power, should it have 3 solutions. (2, 12, -12?)

sin^2 x + cos x


^----I feel that there is a chain rule hidden but I'm not quite sure on how to aproach it (sin^2 x)


Also I have a question on identifying where each function is increasing or decreasing, find the extrema if it exists. (homework question)

k(x) = x^3 -12x on [0,4]

k(x) = (-2x^3 )(x-4)
I appreciate any help!
Joe

 

[Daniel_Feldman]

How do you solve for the critical pts. of these two functions?

.25t^4 - 8t

^---- find the derivitive and set it to zero, but because Its to the 4th power, should it have 3 solutions. (2, 12, -12?)

sin^2 x + cos x


^----I feel that there is a chain rule hidden but I'm not quite sure on how to aproach it (sin^2 x)


Also I have a question on identifying where each function is increasing or decreasing, find the extrema if it exists. (homework question)

k(x) = x^3 -12x on [0,4]

k(x) = (-2x^3 )(x-4)
I appreciate any help!
Joe

f(t)=.25t^4 - 8t
f'(t)=t^3-8

t^3-8=0

Now solve for t.


f(x)=sin^2 x + cos x

=(sinx)^2+cosx

Power rule/Chain rule on the sin...

f'(x)=2(sinx)(cosx)-sinx=0

sinx(2cos(x)-1)=0

sinx=0
cosx=1/2

Solve for x.

k(x) = x^3 -12x on [0,4]

Find k'(x) and where it equals 0. Then find the intervals where k' is positive (k is increasing) or negative (k is decreasing).

Relative maximum occurs where k'(x) changes from positive to negative, while relative minimum occurs where k'(x) changes from negative to positive.

 

[Joey29]

Thankyou

Thanks for your help!