Question

Please help with these!!! I have been trying for hours and it is just not clicking!
It's Calculus by the way.

1) y=5x^4 + 24x^3 + 24x^2 +7 is concave for?

2) The first derivative of the function f is given by f^'=(sin^2(x)/x)-(2/9) How many critical values does f have on the open interval (0,10)

3) If y=3x+6 what is the min. value of (x^3)y

4) If f^''(x)=(x-1)(x+2)^3(x-4)^2, then the graph of f has inflection points when x= 1, -2, or 4 (could be more than one)

Please answer what you can! I would be so grateful you have no idea.

Answer 1

for #1: take the second derivative. The sign of the second derivative is the concavity.

Answer 2

I am having trouble with derivatives. Sounds silly and is madly unfortunate considering that derivatives make up most of Calculus.

Answer 3

you know the rule for derivatives of polynomials?

Answer 4

well for #1 just use the power rule

d/dx x^n is nx^n-1

do this for all the terms....then do it again for the 2nd derivative because the determines concavity

Answer 5

^ like john said.

Answer 6

Okay, thank you. Any clue on the others?

Answer 7

#2... what are critical values?

Answer 8

I haven't the slightest clue. I tried looking it up but nothing was clear in how to find them.

Answer 9

should we assume they are the same as critical points?

Answer 10

So when the tan line is horizontal, or doesn't exist?

Answer 11

yes

Answer 12

Okay, that would make a lot more sense!

Answer 13

for #3, sketch y=3x+6 and (x^3)y

Answer 14

for #4, the graph has an inflection point whenever the second derivative equals zero. They give you the second derivative there, so they basically gave you the answer.