Question

Can someone please explain how to solve this type of question?

Determine the maximum and minimum value of the function f(x)=3x3^x - 1 (I will write out equation)

Answer 1

\[f(x)=3x3^x-1\]

Answer 2

i got f'(x)=3(3^x)+3x(ln3)^3^x as my derivative but I do not know how to simplify it

Answer 3

You're on the right track by finding the derivative, which should be
\[3*3^x + 3x(3^xln3)\]
Now what you need to do is set this derivative equal to 0, and that will give you the x value.

Answer 4

would the x value just be zero?

Answer 5

Try plugging it in and see. If you plug in 0, then you get 3. What we're looking for is when the derivative is equal to 0.

Answer 6

oh ok so order of operations? I think i'm doing this wrong so far:
\[0=3(3^x)+3x(3xln3)\]
\[0=9^x+9x^23xln3\]

Answer 7

i dont know how to isolate x

Answer 8

Your derivative isn't quite right, it should be
\[3\cdot3^x+3x\cdot3^xln3\]
Maybe that'll help.

Answer 9

Hint: You have a common factor of 3*3^x in both terms. Factor that out

Answer 10

Oh thanks. So now I have this as my x value: -1/ln3

Answer 11

would i now find the second derivative and then substitute the x value into the function of the second derivative?

Answer 12

No. that's the end of the problem. This is the minimum value of the function. There is no maximum.

Answer 13

ok thanks! also, how would you know if there is no minimum or no maximum?

Answer 14

just plot the graph using wolfram