Question

Let f(x) = 13 x^3 - 10 x^2

Find all values of x (if any) for which f may have a relative maximum or a relative minimum.

Answer 1

differentiate and equate to 0
solve for x to find x coods of turning points
identify the nature of turning points

Answer 2

turning points?

Answer 3

i dont think we're that far yet

Answer 4

yea - max, minm or points of inflection on the graph of the function
- you are learning calculus right?

Answer 5

oh ok and yes calculus

Answer 6

f'(x) = 39x^2 - 20x = 0
x(39x - 20) = 0
x = 0 or 20/39

Answer 7

so there is a t.p. at x=0 and x = 20/39
to find their nature
find f"
can you continue from here?

Answer 8

find the 2nd deriv from the first deriv equation?

Answer 9

right

Answer 10

yeah i can go from here but im doing my homework and they are asking me for something odd like
. g'(x)>0 for the following values of x: and its multiple choice like a<x<b

Answer 11

oh -maybe they are asking you to find maxm or minm by the sign of the derivative either side of the two values of x
for example if at x = 0 f'(x) is >0 just before that point and < 0 just after then x=0 is a maximum

Answer 12

well ive found the critical points but i dont know how to implement them to find what they're looking for

Answer 13

can you post the original question?

Answer 14

here it is : Let f(x) = 13 x^3 - 10 x^2

Find all values of x (if any) for which f may have a relative maximum or a relative minimum.

Give answers in increasing order (smallest first)
there should be two answers

Answer 15

ok - we've done that. they are x = 0 and x = 20/39 They haven't asked us to identify which is max or min though we can do that if we like.

Answer 16

f"(x) = 78x - 20
f"(0) is < 0 so this is a maxm
f(20/39) is >0 so this minm.

Answer 17

yeah i plugged in x=0 and x = 20/39 and it says its right

Answer 18

thank you very much, you saved my life lol

Answer 19

yw