Question

Let f be the function given by f9x0=x^3-5x^2+3x+k, where k is a constant
a. On what interval is f increasing?
b. On what interval is the graph concave downwards
c. Find the value of k for which f has 11 as its relative minimum.

Answer 1

looks derivable to me

Answer 2

i function is increasing when its slope is increaseing; and slope is defined to be the first derivative

Answer 3

so, what would the first derivative be for this?

Answer 4

okay so then you get uhm 3x^2-10x+3? K wud be zero because its a constant right?

Answer 5

good

Answer 6

this is a quadratic and when it is positive our function is increasing; so lets use our knowledge of quadritics to determine the zeros for this new functions

Answer 7

(x-3) (3x-1) if you want to verify that

Answer 8

so ur basically solving for the x values and that'll be your critcal number ?then you test it oh okay got that nd then it would be the second deriv for the concaveity ?

Answer 9

so ur basically solving for the x values and that'll be your critcal number ?then you test it oh okay got that nd then it would be the second deriv for the concaveity ?

Answer 10

yes

Answer 11

second derivative is inflection; the points where the concavity changes

Answer 12

i always just name it cave up or cave down depending on the sign to avoid confusion in my mind :)

Answer 13

ohokay thank you ^^ and alright so i get that part but i dont get what the part c is looking for like i dont know what to do for it ><

Answer 14

determine the zero of the first derivaitive; the 3 will be our low point

Answer 15

when x=3, when does the f(3) = 11?

Answer 16

for which value of k that is

Answer 17

\[11 = (3)^3-5(3)^2+3(3)+k\]
and solve for k

Answer 18

oh okay thank you and sorry it like froze

Answer 19

'sok, yw :)